Inclusion Criteria:

          -  FLT3-ITD mutated patients with relapsed/refractory AML (up to four prior therapeutic
             regimens for AML i.e. up to salvage 4 AML), including patients who may have been
             previously exposed to prior FLT3-inhibitor/s other than quizartinib (stem cell
             transplant [SCT] or stem cell therapy for patients who previously underwent SCT/stem
             cell therapy in remission will not be considered a salvage regimen)

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2

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

          -  Serum direct bilirubin =< 1.5 x upper limit normal (ULN) (or =< 3.0 x ULN if deemed to
             be elevated due to leukemia)

          -  Alanine aminotransferase and/or aspartate aminotransferase (aspartate transaminase) =<
             2.5 x ULN (or =< 5.0 x ULN if deemed elevated due to leukemia)

          -  Subjects with documented Gilbert's Syndrome may have a total bilirubin > 1.5 x ULN

          -  Potassium levels should be within institutional normal limits

          -  Magnesium levels should be within institutional normal limits

          -  Calcium (normalized for albumin) levels should be within institutional normal limits

          -  Adequate renal function as demonstrated by a serum creatinine =< 1.8

          -  Patients must provide written informed consent

          -  With the exception of patients with rapidly proliferative disease, the interval from
             prior treatment to time of initiation of venetoclax and quizartinib administration
             will be at least 14 days or at least 5 half-lives (whichever is shorter) for
             cytotoxic/noncytotoxic agents. The half-life for the therapy in question will be based
             on published pharmacokinetic literature (abstracts, manuscripts, investigator
             brochures, 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:

               -  Intrathecal (IT) therapy for patients with controlled central nervous system
                  (CNS) leukemia at the discretion of the principal investigator (PI). Controlled
                  CNS leukemia is defined by the absence of active clinical signs of CNS disease
                  and no evidence of CNS leukemia on the most recent 2 simultaneous cerebrospinal
                  fluid (CSF) evaluations

               -  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 on
                  therapy. These medications will be recorded in the case-report form

          -  Baseline ejection fraction by echocardiogram (ECHO) or multigated acquisition scan
             (MUGA) must be >= 50%

          -  Women of non-childbearing potential are those who are postmenopausal greater than 1
             year or who have had a bilateral tubal ligation or hysterectomy

          -  Women of childbearing potential must agree to have a negative serum or beta human
             chorionic gonadotropin (beta-hCG) pregnancy test result within 7 days prior to the
             first dose of study drugs and must agree to use an effective contraception method
             during the study and for 90 days following the last dose of the study. Men who have
             partners of childbearing potential must agree to use an effective contraceptive method
             during the study and for 90 days following the last dose of study drug

        Exclusion Criteria:

          -  Subject has t(8;21) or inv(16) karyotype abnormalities

          -  Subject has acute promyelocytic leukemia (French-American-British Class M3 AML)

          -  Prior exposure to quizartinib at any time in the past

          -  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 allergy or hypersensitivity to quizartinib, venetoclax or any of
             their components

          -  Subject with a known history of being human immunodeficiency virus (HIV) positive (due
             to potential drug-drug interactions between antiretroviral medications and venetoclax,
             as well as anticipated venetoclax mechanism-based lymphopenia that may potentially
             increase the risk of opportunistic infections)

               -  Note: HIV testing is not required

          -  Subject has consumed grapefruit, grapefruit products, Seville oranges (including
             marmalade containing Seville oranges) or star fruit within 3 days prior to the
             initiation of study treatment

          -  Subject has a significant history of renal, neurologic, psychiatric, endocrinologic,
             metabolic, immunologic, hepatic, cardiovascular disease, or any other medical
             condition that in the opinion of the investigator and/or the PI would adversely affect
             his/her participating in this study. Patients who have had any major surgical
             procedure within 14 days of day 1

          -  Subject has a malabsorption syndrome or other condition that precludes enteral route
             of administration

          -  Subject exhibits evidence of other clinically significant uncontrolled condition(s)
             including, but not limited to: a. Uncontrolled systemic infection requiring
             intravenous (IV) therapy (viral, bacterial or fungal). Infections controlled on
             concurrent anti-microbial agents are acceptable, and anti-microbial prophylaxis per
             institutional guidelines is acceptable. Patients with neutropenic fever considered
             infection related should be afebrile for at least 72 hours prior to first dose

          -  Subject has a history of other malignancies within 1 year prior to study entry, with
             the exception of:

               -  Adequately treated in situ carcinoma of the cervix uteri or carcinoma in situ of
                  breast

               -  Basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin

               -  Previous malignancy confined and surgically resected (or treated with other
                  modalities) with curative intent

               -  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 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 hepatitis B virus (HBV) (i.e., hepatitis B surface antigen
             negative [HBs Ag-], and hepatitis B surface antibody positive [anti-HBs+]) may
             participate

          -  Female subjects who are pregnant or breastfeeding

          -  Impaired cardiac function including any of the following:

               -  Screening electrocardiogram (ECG) with a corrected QT (QTc) > 450 msec. The QTc
                  interval will be calculated by Fridericia's correction factor (QTcF) at screening
                  and on day 1 prior to the first dose of quizartinib. The QTcF will be derived
                  from the average QTcF in triplicate. If QTcF > 450 msec on day 1, quizartinib
                  will not be given.

               -  Patients with congenital long QT syndrome

               -  History or presence of sustained ventricular tachycardia requiring medical
                  intervention within 3 months prior to starting study drug

               -  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) within 3 months prior to starting study drug

               -  Sustained heart rate of < 50/minute on screening or day 1 ECG

               -  Right bundle branch block + left anterior hemiblock (i.e. bifascicular block)

               -  Isolated right bundle branch block (RBBB) will not be an exclusion criterion

               -  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
                  within 3 months prior to starting study drug

               -  Atrial fibrillation documented within 2 weeks prior to first dose of study drug

               -  Patients who are actively taking CYP3A inducers. CYP3A4 inducers should be
                  stopped at least 3 days prior to the first dose of quizartinib and are prohibited
                  at any time on study. Moderate and strong CYP3A4 inhibitors should be stopped at
                  least 3 days prior to the first dose of quizartinib and are prohibited during
                  cycle 1. Moderate (but not strong) CYP3A4 inhibitors may be used with the below
                  dose reductions of venetoclax after cycle 1. Patients may receive weak CYP3A4
                  inhibitors at any time on study. The venetoclax and quizartinib doses do not need
                  to be adjusted for weak CYP3A4 inhibitors

               -  Patients who require treatment with concomitant drugs that prolong QT/QTc
                  interval. QT/QTc prolonging drugs should be stopped at least 3 days prior to the
                  first dose of quizartinib and are prohibited at any time on study

               -  Known family history of congenital long QT syndrome