Registration Criteria:

          -  Any patient undergoing bone marrow biopsy with suspicion of or known diagnosis of
             acute myeloid leukemia (AML) will be asked to sign a Prescreening Consent to allow for
             centralized testing of bone marrow/peripheral blood samples.

        Randomization Eligibility Criteria:

          -  Patient must have previously untreated FLT3 mutated Non M3 AML (FLT3-TKD or FLT3-ITD
             allowed).

             ° Standard of care induction 7+3 chemotherapy may start prior to randomization using
             same regimen and doses as defined in the protocol while awaiting prescreening test
             results.

          -  Patient must have had no prior systemic therapy for AML, except as noted below:

               -  Hydroxyurea and emergent leukapheresis or preemptive treatment with retinoic acid
                  prior to exclusion of Acute Promyelocytic Leukemia (APL) allowed.

               -  Prior therapy for myelodysplastic syndrome (MDS) or myeloproliferative neoplasms
                  (MPN) (e.g., thalidomide or lenalidomide, interferon, jakafi, cytokines,
                  5-azacytidine or decitabine, histone deacetylase inhibitors).

               -  Initiation of standard of care 7+3 induction chemotherapy using same regimen and
                  doses as defined in protocol while awaiting prescreening test results

          -  Patient may not have received hypomethylating agent within 21 days.

          -  Patient may not have M3 AML.

          -  Patient may not have AML with known Core Binding Factor -t(8;21), inv(16), t(16;16).

          -  Patient may not have known active Central Nervous System (CNS) leukemia.

             ° Prophylaxis with intrathecal chemotherapy is allowed prior to or during
             induction/consolidation.

          -  Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of
             0-3.

          -  Patient must be age ≥ 18 years to ≤ 70 years.

          -  Patient must be able to understand and willing to sign Institutional Review Board
             (IRB)-approved informed consent.

          -  Patient must be willing to provide mandatory bone marrow and blood samples for
             research.

          -  Patient must have adequate organ function as measured by the following criteria,
             obtained ≤ 48 hours prior to randomization except ECG and left ventricular ejection
             fraction (LVEF) which can be done ≤ 2 weeks prior to randomization:

               -  Serum creatinine ≤ 1.5x institutional upper limit of normal (ULN), or if serum
                  creatinine outside normal range, then glomerular filtration rate (GFR) >40 mL/min
                  as measured by Cockcroft-Gault formula.

               -  Alanine Aminotransferase (ALT) and Aspartate Aminotransferase (AST) ≤ 3x ULN,
                  unless secondary to leukemia.

               -  Serum total or direct bilirubin <2 mg/dL, unless due to Gilbert's, hemolysis or
                  leukemic infiltration.

               -  Fridericia-Corrected QT Interval (QTcF) interval ≤ 500 msec (using Friderica's
                  correction).

               -  Left Ventricular Ejection Fraction >45%.

          -  The patient may not be known to have hypokalemia and/or hypomagnesemia that does not
             respond to supplementation.

          -  A female patient is eligible to participate if she is not pregnant and at least one of
             the following conditions apply:

               -  Not a woman of childbearing potential (WOCBP) OR

               -  WOCBP who agrees to follow the contraceptive guidance throughout the treatment
                  period and for at least 180 days after the final study drug administration.

          -  Female patient must agree not to breastfeed or donate ova starting at treatment and
             throughout the study period, and for at least 180 days after the final study drug
             administration.

          -  A male patient must agree not to donate sperm starting at treatment and throughout the
             study period, and for at least 120 days after the final study drug administration.

          -  A male patient with female partner(s) of child-bearing potential must agree to use
             contraception during the treatment period, and for at least 120 days after the final
             study drug administration.

          -  Male patient with a pregnant or breastfeeding partner(s) must agree to remain
             abstinent or use a condom for the duration of the pregnancy or time partner is
             breastfeeding throughout the treatment period, and for at least 120 days after the
             final study drug administration.

          -  Patient may not have another malignancy that could interfere with the evaluation of
             safety or efficacy of this combination.

          -  Patient may not have a history of Long QT Syndrome.

          -  Patient may not have evidence of uncontrolled angina, severe uncontrolled ventricular
             arrhythmias, electrocardiographic evidence of acute ischemia, or congestive heart
             failure (CHF) New York Heart Association (NYHA) Class 3 or 4. Patient may also not
             have a history of CHF NYHA Class 3 or 4 in the past, unless a prescreening
             echocardiogram (ECHO) or multigated acquisition scan (MUGA) performed within 2 weeks
             prior to study entry with results of left ventricular ejection fraction >45%.

          -  Patient may not have had major surgery or radiation therapy within 4 weeks of
             registration.

          -  Patient may not require treatment with concomitant drugs that are strong inducers of
             CYP3A.

          -  Patient with a known allergy to any of the study medications, their analogues, or
             excipients in the various formulations of any agent are not eligible.

          -  Patient with known gastrointestinal (GI) disease or prior GI procedure that could
             interfere with the oral absorption or tolerance of gilteritinib or midostaurin
             including difficulty swallowing are not eligible.

          -  Patient with any serious medical or psychiatric illness that could, in the
             investigator's opinion, potentially interfere with the completion of the treatment
             according to the protocol are not eligible.

          -  Patient may not participate in any other therapeutic clinical trials, including those
             with other investigational agents not included in this trial during treatment on this
             study without prior approval from PrECOG.