Venetoclax and Quizartinib in Treating Patients With FLT3-mutated Recurrent or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * FLT3-ITD mutated patients with relapsed/refractory AML (up to four prior therapeutic regimens for AML i.e. up to salvage 4 AML), including patients who may have been previously exposed to prior FLT3-inhibitor/s other than quizartinib (stem cell transplant \[SCT\] or stem cell therapy for patients who previously underwent SCT/stem cell therapy in remission will not be considered a salvage regimen) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Serum direct bilirubin =\< 1.5 x upper limit normal (ULN) (or =\< 3.0 x ULN if deemed to be elevated due to leukemia) * Alanine aminotransferase and/or aspartate aminotransferase (aspartate transaminase) =\< 2.5 x ULN (or =\< 5.0 x ULN if deemed elevated due to leukemia) * Subjects with documented Gilbert's Syndrome may have a total bilirubin \> 1.5 x ULN * Potassium levels should be within institutional normal limits * Magnesium levels should be within institutional normal limits * Calcium (normalized for albumin) levels should be within institutional normal limits * Adequate renal function as demonstrated by a serum creatinine =\< 1.8 * Patients must provide written informed consent * With the exception of patients with rapidly proliferative disease, the interval from prior treatment to time of initiation of venetoclax and quizartinib administration will be at least 14 days or at least 5 half-lives (whichever is shorter) for cytotoxic/noncytotoxic agents. The half-life for the therapy …