A Phase Ib/II Study of Venetoclax in Combination With Quizartinib in FLT3-Mutated Acute Myelogenous Leukemia (AML)

• 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 in question will be based on published pharmacokinetic literature (abstracts, manuscripts, investigator brochures, or drug-administration manuals) and will be documented in the protocol eligibility document. The use of chemotherapeutic or anti-leukemic agents is not permitted during the study with the following exceptions:

‣ Intrathecal (IT) therapy for patients with controlled central nervous system (CNS) leukemia at the discretion of the principal investigator (PI). Controlled CNS leukemia is defined by the absence of active clinical signs of CNS disease and no evidence of CNS leukemia on the most recent 2 simultaneous cerebrospinal fluid (CSF) evaluations

⁃ Use of one dose of cytarabine (up to 2 g/m\^2) or hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and on therapy. These medications will be recorded in the case-report form

• Baseline ejection fraction by echocardiogram (ECHO) or multigated acquisition scan (MUGA) must be \>= 50%

• Women of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy

• Women of childbearing potential must agree to have a negative serum or beta human chorionic gonadotropin (beta-hCG) pregnancy test result within 7 days prior to the first dose of study drugs and must agree to use an effective contraception method during the study and for 90 days following the last dose of the study. Men who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 90 days following the last dose of study drug