Venetoclax and HMA Treatment of Older and Unfit Adults With FLT3 Mutated Acute Myeloid Leukemia (AML) (A MyeloMATCH Treatment Trial)

Inclusion Criteria: * Patient must be ≥ 60 years of age or adults ˂ 60 who in the opinion of the treating physician are better served by azanucleoside-based therapy rather than intensive, cytarabine-based induction based on clinical status (i.e., performance status), organ dysfunction, or disease biology * Patient must have a morphologically confirmed diagnosis of AML as determined by the site and confirmed by the treatment verification team, excluding acute promyelocytic leukemia (APL) with PML-RARA, AML with RUNX1-RUNX1T1, or AML with CBFB-MYH11 * Patient must have no prior therapy for AML with the exception of hydroxyurea, all-trans retinoic acid (ATRA), cytarabine-based emergency therapy or leukapheresis to ensure white blood cells (WBC) \< 25,000/mm\^3 prior to starting venetoclax treatment * Patient must have no prior therapy with hypomethylating agents or FLT3 inhibitors * Patient must have the FLT3-ITD, D835, or I836del mutation based on MYELOMATCH Protocol * Patient must be assigned to this protocol by the MYELOMATCH Protocol * Patient must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used All patients of childbearing potential must have a blood test or urine study within 14 days prior to randomization to rule out pregnancy A patient of childbearing potential is defined as anyone, regardless of whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Patients must not expect to conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study. Contraception measures must continue for 30 days after the last dose of venetoclax for all patients who are able to conceive or father children and for 6 months after the last dose of gilteritinib for patients of childbearing potential and for 4 months after the last dose of gilteritinib for male patients with partners of childbearing potential. Patient must not breastfeed during treatment and for 2 months after treatment ends * Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible * Total bilirubin ≤ 2 X institutional upper limit of normal (ULN), unless thought to be elevated due to disease involvement or Gilbert's syndrome, in which case bilirubin ≤ 3 x ULN is allowed (must be obtained ≤ 14 days prior to randomization) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN (must be obtained ≤ 14 days prior to randomization) * Creatinine clearance ≥ 30 mL/min (must be obtained ≤ 14 days prior to randomization) * Either measured or estimated by Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) Creatinine Equation (2021) * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of randomization are eligible for this trial * Patients who meet the criteria below must have had an electrocardiogram (ECG) performed with a corrected QT interval using Fridericia's correction (QTcF) interval within normal limits: * Patient \< 75 years old with a history of cardiac arrythmia, atrial fibrillation, or irregular QTcF interval OR * Patient \< 75 years old with known genetic predisposition to long QT syndrome OR * Any patient ≥ 75 years old OR * Any patient at risk for electrolyte abnormalities, including tumor lysis syndrome * Normal limits are QTcF ≤ 450 ms for males and QTcF ≤ 460 ms for females. Corrected QT interval method (QTcF) may follow institutional standards * NOTE: Since older patients and patients with cardiac disease are at risk for prolonged QTcF and many will require supportive care with agents that affect the QTcF, an ECG is recommended if clinically indicated as noted above. If the QTcF is prolonged (\> 450 ms for males and \> 460 ms for females), they should be treated on the Tier Advancement Pathway (TAP) instead of MM1OA-EA02. In patients where ECG is not clinically indicated, QTcF does not need to be documented * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patient must not have the medical necessity for ongoing treatment with a strong CYP3A4 inducing drug * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2 or better * Patient must not have an uncontrolled infection