Quizartinib With Azacitidine or Cytarabine in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia or Myelodysplastic Syndrome

Inclusion Criteria: * PHASE I * Refractory or relapsed disease defined as follows: patients with MDS or chronic myelomonocytic leukemia (CMML) should have failed prior therapy (e.g., with a hypomethylating agent, clofarabine, and/or with lenalidomide); patients with AML should have failed any prior induction therapy or have relapsed after prior therapy; patients (any age) with MDS or CMML who received therapy with a hypomethylating agent and progress to AML are eligible at the time of diagnosis of AML regardless any prior therapy for AML. The World Health Organization (WHO) classification will be used for AML; patients with any of the eligible diagnoses who have received no prior therapy are eligible if not candidates to receive standard intensive therapy (i.e., high-dose cytarabine-based chemotherapy). * Patients are eligible regardless of their FLT3 mutation status. * PHASE II * COHORT 2A: Patients with MDS, CMML or AML who are either: age 60 years or older and newly diagnosed, previously untreated. Prior therapy with hydroxyurea or single agent ara-C for the purpose of control of white blood cells (WBC) is acceptable.; age 18 years or older and with refractory or relapse disease who have received no more than one prior treatment regimen and will be receiving first salvage. For this purpose, a second induction cycle with the same drugs used during the first cycle, consolidation chemotherapy or stem cell transplant in complete remission (CR) (or complete response with incom…