A Phase 1b Multi-center Study of the FLT3 Inhibitor Gilteritinib in Combination With the IDH1 Inhibitor Ivosidenib or the IDH2 Inhibitor Enasidenib for Patients With Relapsed or Refractory Acute Myeloid Leukemia Who Have Co-occurring FLT3/IDH1 or FLT3/IDH2 Mutations

Inclusion Criteria: * Adult patient is ≥18 years of age at the time of signing the informed consent form (ICF) * Patient is willing and able to adhere to the study visit schedule and other protocol requirements. * Patient has a confirmed diagnosis of relapsed AML as per World Health Organization (2016) guidelines. Patients in morphologic remission with the reappearance of MRD are also eligible to participate OR the patient has refractory AML as defined below: 1. For patients who received intensive induction chemotherapy they must have persistent AML (defined as overt disease with over 5% myeloblasts) after at least one cycle of intensive induction OR 2. For patients treated with low intensity therapy, the patient must be refractory to treatment with a single agent hypomethylating agent (HMA) or low dose cytarabine (LDAC) (at least two cycles) or an HMA/LDAC in combination with venetoclax (at least one cycle) or another standard of care therapy (e.g. gemtuzumab ozogamicin, glasdegib/LDAC). * Patient has relapsed or refractory AML with dually mutant IDH2/FLT3, IDH1/FLT3 (ITD or TKD) , or other FLT3 mutation sensitive to gilteritinib. a. A Patient receiving enasidenib or ivosidenib as a single agent who acquires a FLT3 mutation during treatment or a patient on single agent gilteritinib who acquires an IDH2 or IDH1 mutation during treatment is eligible to participate in this study * Patient has documentation of FLT3 and IDH1 or IDH2 mutation in bone marrow or blood at time of relapsed/refractory status confirmed by next-generation sequencing (NGS) and/or polymerase chain reaction (PCR) or fragment length analysis within the previous 30 days by a local CLIA approved test. * Patient has Eastern Cooperative Oncology Group (ECOG) performance status of 0-3. * Patient should have adequate renal function, defined as creatine clearance ≥30mL/min calculated using the Cockcroft-Gault equation or a serum creatinine less than 2.0. * Patient should have adequate hepatic function, defined as aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3x the upper limit of normal (ULN) and serum direct bilirubin ≤ 2.0 x ULN. Patient with leukemic organ involvement as assessed by the study investigator, must have a serum direct bilirubin ≤ 5.0 x ULN. * Patient who has previously had an autologous or allogeneic stem cell transplant for AML is allowed on study. * Female patient of childbearing potential must have had a negative pregnancy test within 7 days of initiation of dosing and must agree to use two acceptable methods of birth control while on treatment. A woman must agree to remain on a highly effective method throughout the study and for at least 6 months after the last dose of study drug. A female is considered fertile following menarche and until becoming postmenopausal unless permanently sterile. * Male participants with female partners of childbearing potential are eligible for participation in the study if they agree to the following during treatment and until the end of relevant systemic exposure defined as 6 months after final drug administration. Exclusion Criteria: * Patient has a diagnosis of acute promyelocytic leukemia (APL). * Patient on any other investigational anti-cancer agents. * Patient has active uncontrolled systemic fungal, bacterial, or viral infection. * Patient has presence of any other condition that may increase the risk associated with study participation, and in the opinion of the investigator, would make the patient inappropriate for entry into the study. * Patient has immediate life-threatening, severe complications of leukemia such as uncontrolled bleeding, pneumonia with hypoxia or shock, and/or severe disseminated intravascular coagulation. * Patient has significant active cardiac disease within 6 months prior to the start of study treatment, including New York Heart Association (NYHA) class III or IV congestive heart failure; acute coronary syndrome (ACS); and/or ischemic stroke. * Patient has left ventricular ejection fraction (LVEF) \< 40% by echocardiogram (ECHO) or multi-gated acquisition (MUGA) scan obtained within 28 days prior to the start of study treatment. * Patient is known to have dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered orally. * Patient has a medical history of progressive multifocal leukoencephalopathy. * Patient has QTc interval (i.e., Fridericia's correction \[QTcF\]) ≥ 450 ms (mean of triplicate ECG) or other factors that increase the risk of QT prolongation or ventricular arrhythmic events (e.g. family history of long QT interval syndrome). Patients with a QTcF over 450 ms due to a bundle branch block or a pacemaker may participate in the study with approval of the study principal investigator. * Patient has active graft-versus-host disease. However patients with isolated skin GVH controlled with topical steroids are eligible to participate * Female patient who is pregnant or lactating.