Azacitidine, Venetoclax, and Gilteritinib in Treating Patients With Recurrent/Refractory FLT3-Mutated Acute Myeloid Leukemia, Chronic Myelomonocytic Leukemia, or High-Risk Myelodysplastic Syndrome/Myeloproliferative Neoplasm

Inclusion Criteria: * Diagnosis: * Phase I cohort: Adults ≥ 18 years with relapsed/refractory FLT3-mutated AML or CMML or other MDS/MPN that is intermediate-2 or high-risk by the International Prognostic Scoring System * Phase II cohort A: Adults ≥ 18 years with newly diagnosed FLT3-mutated AML * Phase II cohort B: Adults ≥ 18 years with relapsed/refractory FLT3-mutated AML or CMML or other MDS/MPN that is intermediate-2 or high-risk by the International Prognostic Scoring System * For all cohorts, patients with either FLT3-internal tandem duplication (FLT3-ITD) or FLT3 D835 mutations will be eligible * Performance status ≤ 3 (Eastern Cooperative Oncology Group \[ECOG\] scale) * Total serum bilirubin ≤ 2.5 x upper limit of normal (ULN), unless due to Gilbert's syndrome, hemolysis or the underlying leukemia approved by the principal investigator (PI) * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 3 x ULN, unless due to the underlying leukemia approved by the PI * Creatinine clearance ≥ 30 mL/min * Ability to swallow * Signed informed consent Exclusion Criteria: * Prior therapies: * Phase I cohort: No restriction based on prior therapies * Phase II cohort A: Patients with prior therapy for AML are not eligible. Prior therapy for antecedent hematologic disorder is allowed. Prior hydroxyurea or cytarabine given for purposes of cytoreduction is also allowed. Prior all trans-retinoic acid given for presumed acute promyelocytic leukemia is al…