Phase I Trial of AZD1775 and Belinostat in Treating Patients With Relapsed or Refractory Myeloid Malignancies or Untreated Acute Myeloid Leukemia

Inclusion Criteria: * Patients must have one of the following, histologically or cytologically confirmed: * Acute myeloid leukemia (AML) \[non- acute promyelocytic leukemia (APL) AML\] * If previously treated: * AML that is relapsed or refractory to at least one prior line of therapy * If previously untreated, must meet all of the following: * \>= 60 years of age * Secondary or therapy-related AML * Does NOT bear favorable cytogenetic and/or molecular features, eg, core-binding factor abnormalities, FLT3 Internal Tandem Duplication (FLT3-ITD) negative/NPM1 mutated, biallelic CCAAT/enhancer binding protein alpha (CEBPA) mutation without FLT3-ITD * Chronic myeloid leukemia blast crisis (CML-BC) * Relapsed or refractory to at least one Bcr-Abl-TKI-containing regimen * Myelodysplastic syndrome (MDS), must meet all of the following: * Higher risk MDS \[intermediate-2 or high risk by the original International Prognostic Scoring System (IPSS)\] * Relapsed, refractory, or intolerant to at least one prior line of therapy containing hypomethylating agents (deoxyribonucleic acid \[DNA\] methyltransferase inhibitors) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%) * Total bilirubin =\< 1.5 × upper limit of normal (ULN) for the laboratory unless resulting from hemolysis * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum…