A Phase I/II Study of Gilteritinib and Momelotinib for Patients With Relapsed or Refractory FLT3-Mutated Acute Myeloid Leukemia

Inclusion Criteria: 1. Diagnosis: a) Adults ≥18 years with relapsed/refractory FLT3-mutated AML. Participants with either FLT3-ITD or FLT3 D835/D836 mutations will be eligible 2. Performance status ≤3 (ECOG Scale). 3. Adequate liver and renal function as defined by the following criteria: 1. Total serum bilirubin ≤ 2 x upper limit of normal (ULN), unless due to Gilbert's syndrome, hemolysis or the underlying leukemia approved by the PI 2. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 3 x ULN, unless due to the underlying leukemia approved by the PI d) Creatinine clearance ≥ 30 mL/min 4. Willingness to use adequate contraception prior to study entry, for the duration of study participation, and for 4 months after completion of study participation. For women of childbearing potential, adequate methods of contraception include: complete abstinence, hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), intrauterine device (IUD), tubal Ligation or hysterectomy, participants/partner post vasectomy, implantable or injectable contraceptives, and condoms plus spermicide 5. Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 1. Congenital long QT syndrome or QTcF \>450 msec. Repeat EKGs after correction of electrolytes or discontinuation of QT prolonging medications are allowed to meet entry criteria. In cases where QTcF \>450 msec is considered to be falsely increased due to inaccurate automated reading and not clinically significant (e.g. due to bundle branch block), participants are still eligible if cardiologist reviews and documents that QTcF is ≤ 450 msec when manually measured. 2. Active serious infection not controlled by oral or intravenous antibiotics (e.g. persistent fever or lack of improvement despite antimicrobial treatment). 3. Active Class III-V cardiac failure as defined by the New York Heart Association Functional Classification. 4. Active central nervous system leukemia 5. Child-Turcotte-Pugh class C cirrhosis 6. Known human immunodeficiency virus (HIV) seropositive. 7. Known hepatitis B surface antigen seropositive or known or suspected active hepatitis C infection Note: Participants who have isolated positive hepatitis B core antibody (ie, in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load. Participants who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load. 8. Participants with a prior or concurrent malignancy whose natural history or treatment is not anticipated to interfere with the safety or efficacy assessment of the investigational regimen may be included only after discussion with the PI 9. Treatment with any investigational antileukemic agents or chemotherapy agents in the last 7 days before study entry, unless full recovery from side effects has occurred or participant has rapidly progressive disease judged to be life-threatening by the investigator. Prior recent treatment with corticosteroids, hydroxyurea and/or cytarabine (given for cytoreduction) permitted. 10. Inability to swallow 11. Unable or unwilling to sign informed consent 12. Pregnant women will not be eligible; A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies: i. Is a woman of nonchildbearing potential (WONCBP), OR ii. Is a woman of childbearing potential (WOCBP) and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), with low user dependency, during the intervention period and for at least 4 month after the last dose of study drug. 13. Participants with psychiatric illness/social situations that would limit compliance with study requirements. 14. History of allergic reactions attributed to compounds of similar chemical or biologic composition to gilteritinib, momelotinib or other agents used in study.