Inclusion Criteria:

          -  Diagnosis of 1) AML (World Health Organization [WHO] classification definition of >=
             20% blasts) excluding acute promyelocytic leukemia (APL) or 2) MDS with > 10% blasts
             (defined by the International Prognostic Scoring System [IPSS] classification).

          -  For frontline Cohort: Patients aged >= 60 years old who are not candidates for
             intensive induction therapy and agree to receive the proposed combination therapy will
             be enrolled.

          -  Not considered candidates for intensive remission induction chemotherapy at time of
             enrollment based on EITHER:

               -  75 years of age OR

               -  < 75 years of age with at least 1 of the following:

                    -  Poor performance status (Eastern Cooperative Oncology Group [ECOG]) score of
                       2-3.

                    -  Clinically significant heart or lung comorbidities, as reflected by at least
                       1 of:

                         -  Left ventricular ejection fraction (LVEF) =< 50%.

                         -  Lung diffusing capacity for carbon monoxide (DLCO) =< 65% of expected.

                         -  Forced expiratory volume in 1 second (FEV1) =< 65% of expected.

                         -  Chronic stable angina or congestive heart failure controlled with
                            medication.

               -  Liver transaminases > 3 x upper limit of normal (ULN).

               -  Other contraindication(s) to anthracycline therapy (must be documented).

               -  Other comorbidity the investigator judges incompatible with intensive remission
                  induction chemotherapy, which must be documented and approved by the principal
                  investigator (PI).

          -  Patients with newly diagnosed AML with poor risk complex karyotype and/or TP53
             deletions/mutations equal or younger than 60 year old

          -  For relapsed cohort: Patients aged >= 18 years old. (Patients who are candidates for
             relapse cohort will be enrolled into the study regardless of their fitness for
             intensive chemotherapy). (a) Patients with relapsed/refractory AML are eligible if
             they are not eligible for potentially curative therapy such as effective salvage
             therapy or hematopoietic stem cell transplantation or who refuse these options at the
             time of enrollment.

          -  Detection of FLT3-ITD mutation or FLT3-ITD/TKD co-mutations in bone marrow and/or
             peripheral blood samples within 30 days prior to study enrollment.

          -  For frontline cohort: Patients must be chemonaive, i.e. not have received any
             chemotherapy (except hydrea or 1-2 doses of ara-C for transient control of
             hyperleukocytosis) for AML or MDS. They may have received transfusions, hematopoietic
             growth factors or vitamins for an antecedent hematological disorder (AHD) or for AML.
             Temporary prior measures such as apheresis, all-trans-retinoic acid (ATRA), steroids
             or hydrea while diagnostic work-up is being performed are allowed and not counted as a
             prior salvage. Supportive care therapy for MDS (growth factors, transfusions) will not
             be considered as prior therapy for MDS/AML and these patients will be enrolled to the
             frontline cohort of the study if they are otherwise eligible.

          -  For relapsed cohort: Patients who have received at least one prior therapy for AML or
             for MDS with > 10% blasts will be eligible. Patients may have received up to 4 prior
             salvages for AML and/or MDS (defined by the IPSS classification). Prior therapy for
             AML or MDS will be counted as a prior salvage. Patients who receive MDS directed
             therapies considered not purely supportive such as HMAs, lenalidomide, investigational
             therapies, will be enrolled to the salvage cohort if they are otherwise eligible.

          -  In the absence of rapidly progressing disease, the interval from prior treatment to
             time of initiation of protocol therapy will be at least 2 weeks for cytotoxic agents
             or at least 5 half-lives for cytotoxic/noncytotoxic agents. The half-life for the
             therapy in question will be based on published pharmacokinetic literature (abstracts,
             manuscripts, investigator brochure's, or drug-administration manuals) and will be
             documented in the protocol eligibility document

          -  The use of chemotherapeutic or anti-leukemic agents is not permitted during the study
             with the following exceptions: (1) intrathecal (IT) therapy for patients with
             controlled central nervous system (CNS) leukemia at the discretion of the PI a (2) Use
             of one dose of cytarabine (up to 2 g/m^2) or hydroxyurea for patients with rapidly
             proliferative disease is allowed before the start of study therapy and for the first
             four weeks on therapy. These medications will be recorded in the case-report form.

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2.

          -  Serum biochemical values with the following limits unless considered due to leukemia,
             hemolysis or congenital disorder (creatinine < 1.8 mg/dl, total bilirubin < 1.8 mg/dL,
             [serum glutamate pyruvate transaminase (SGPT)] < 2.5 x upper limit of normal).

          -  White blood cell count < 25 x 10^9/L

          -  Potassium, magnesium, and calcium (normalized for albumin) levels should be within
             institutional normal limits.

          -  Ability to take oral medication.

          -  Ability to understand and provide signed informed consent.

          -  Baseline left ventricular ejection fraction by echocardiogram (ECHO) or multigated
             acquisition (MUGA) >= 50%.

          -  Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy
             test within 7 days. Men must agree not to father a child and agree to use a condom if
             his partner is of child bearing potential.

          -  WOCBP must use appropriate method(s) of contraception. WOCBP should use an adequate
             method to avoid pregnancy until at least 3 months after the last dose of
             investigational drug. Women who are not of childbearing potential (i.e., who are
             postmenopausal or surgically sterile) as well as men with azoospermia do not require
             contraception.

          -  Negative urine or serum pregnancy test.

          -  Investigational agents that are not used for treatment of the leukemia per se (e.g.
             anti-infective prophylaxis or therapy) will be allowed. Other supportive care studies
             are allowed, even if under an Investigational New Drug (IND).

        Exclusion Criteria:

          -  Patients with known allergy or hypersensitivity to quizartinib, mannitol, decitabine
             or any of their components.

          -  Prior quizartinib use.

          -  Patients with known uncontrolled CNS leukemia.

          -  Only for frontline cohort: patients who are fit for intensive chemotherapy.

          -  Patients with electrolyte abnormalities at study entry defined as follows: Serum
             potassium < 3.5 mEq/L despite supplementation, or > 5.5 mEq/L Serum magnesium above or
             below the institutional normal limit despite adequate management. Serum calcium
             (corrected for albumin levels) above or below institutional normal limit despite
             adequate management.

          -  Patients with known significant impairment of gastrointestinal (GI) function or GI
             disease that may significantly alter the absorption of quizartinib.

          -  Patients with any other known concurrent severe and/or uncontrolled medical condition
             including but not limited to diabetes, cardiovascular disease including hypertension,
             renal disease, or active uncontrolled infection, which could compromise participation
             in the study. Patients on active antineoplastic or radiation therapy for a concurrent
             malignancy at the time of screening. Maintenance therapy, hormonal therapy, or steroid
             therapy for well-controlled malignancy is allowed.

          -  Patients with a known human immunodeficiency virus (HIV) infection.

          -  Patients with known positive hepatitis B or C infection by serology, with the
             exception of those with an undetectable viral load within 3 months. (Hepatitis B or C
             testing is not required prior to study entry). Subjects with serologic evidence of
             prior vaccination to HBV [i.e., hepatitis B surface antigen [HBs Ag]-, and anti-HBs+]
             may participate.

          -  Patients who have consumed grapefruit, grapefruit products, Seville oranges (including
             marmalade containing Seville oranges) or Starfruit within 3 days prior to the
             initiation of study treatment.

          -  Patients who have had any major surgical procedure within 14 days of day 1.

          -  Impaired cardiac function including any of the following: Screening ECG with a
             Fridericia's correction formula (QTcF) > 450 msec. The QTcF interval will be
             calculated by Fridericia's correction factor (QTcF). The QTcF will be derived from the
             average QTcF in triplicate. Patients are excluded if they have QTcF >= 450. Subjects
             with prolonged QTcF interval in the setting of RBBB (right bundle branch block) may
             participate upon review and approval by the medical monitor. RBBB for patients'
             triplicate EKGs can show false corrected QT (QTc) prolongation; therefore, the
             Cardiology collaborator for this study will manually review to provide an accurate
             reading of the QTc. Patients with congenital long QT syndrome. History or presence of
             sustained ventricular tachycardia requiring medical intervention. Any history of
             clinically significant ventricular fibrillation or torsades de pointes. Known history
             of second or third degree heart block (may be eligible if the patient currently has a
             pacemaker). Sustained heart rate of < 50/minute on pre-entry ECG. Right bundle branch
             block + left anterior hemiblock (bifascicular block). Complete left bundle branch
             block. Patients with myocardial infarction or unstable angina within 6 months prior to
             starting study drug. Congestive heart failure (CHF) New York (NY) Heart Association
             class III or IV. Atrial fibrillation documented within 2 weeks prior to first dose of
             study drug. Patients who are actively taking a strong CYP3A4 inducing medication.

          -  Patients who require treatment with concomitant drugs that prolong QT/QTc interval or
             strong CYP3A4 inhibitors with the exception of antibiotics, antifungals, and
             antivirals that are used as standard of care to prevent or treat infections and other
             such drugs that are considered absolutely essential for the care of the subject or if
             the Investigator believes that beginning therapy with a potentially QTc-prolonging
             medication (such as anti-emetic except for prochlorperazine) is vital to an individual
             subject's care while on study.

          -  Known family history of congenital long QT syndrome.

          -  Patients who are on strong CYP3A4 inhibitor will be excluded.