SNDX-5613 and Gilteritinib for the Treatment of Relapsed or Refractory FLT3-Mutated Acute Myeloid Leukemia and Concurrent MLL-Rearrangement or NPM1 Mutation

Inclusion Criteria: * Signed informed consent must be obtained prior to participation in the study * Age ≥ 18 years at the date of signing the informed consent form (ICF) * Morphologically confirmed diagnosis of the following based on 2022 World Health Organization (WHO) classification: * Relapsed or Refractory Acute Myeloid Leukemia with the following: * Refractory disease classified as having received 2 cycles of intensive induction or 2 cycles of hypomethylating agent (HMA) + Venetoclax with persistent disease of ≥ 5% blasts in the bone marrow and/or reappearance of peripheral blasts * FLT-3 mutated disease of the ITD or TKD subtype, AND * NPM1 mutation, MLL gene rearrangement and any other mutation that has proven HOXA-MEIS1 overexpression (NUP98, UBTF-TD, MLL-PTD and any others that have supporting literature) * Patients must be receiving itraconazole, ketoconazole, posaconazole, or voriconazole (strong CYP3A4 inhibitors) for antifungal prophylaxis for at least 24 hours prior to enrollment and while on SNDX-5613 treatment. Patients must not be receiving any other strong CYP3A4 inhibitors/inducers * Not suitable for immediate myeloablative/intensive chemotherapy based on investigator assessment of age, comorbidities, local guidelines, institutional practice (any or all of these) * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 × upper limit of normal (ULN) * Total bilirubin ≤ 1.5 × ULN (except in the setting of isolated Gilbert syndrome) * Estimated Glomerular Filtration Rate (eGFR) ≥ 60 mL/min/1.73m\^2 (estimation based on Modification of Diet in Renal Disease (MDRD) formula, by local laboratory) * Adequate cardiac function defined as ejection fraction (EF) of ≥50% by echocardiogram or multigated acquisition (MUGA) scan * Patient can communicate with the investigator and has the ability to comply with the requirements of the study procedures * Participants of childbearing potential must agree to have a negative serum pregnancy test at screening and a negative serum or urine pregnancy test on the first day of study treatment * Participants capable of impregnating others who are having intercourse with people of childbearing potential must agree to abstain from intercourse or have their partner use 2 forms of contraception from the screening visit until 90 days after the last dose of study treatment. They must also refrain from sperm donation from the screening visit until 90 days following the last dose of study treatment * Must be able to swallow the study medications * Any prior treatment-related toxicities resolved to ≤ grade 1 prior to enrollment, with the exception of ≤ grade 2 neuropathy or alopecia * Patients are not currently receiving the following therapies or have discontinued therapy based on the time periods below: * Radiation Therapy: At least 60 days from prior total body irradiation (TBI), craniospinal radiation and/or ≥ 50% radiation of the pelvis, or at least 14 days from local palliative radiation therapy (small port) * Stem Cell Infusion: At least 60 days must have elapsed from hematopoietic stem cell transplant (HSCT) and at least 4 weeks must have elapsed from donor lymphocyte infusion (DLI) * Immunotherapy: At least 42 days since prior immunotherapy, including tumor vaccines and checkpoint inhibitors, and at least 21 days since receipt of chimeric antigen receptor therapy or other modified T cell therapy * Antileukemia Therapy\*\*\*: At least 14 days, or 5 half-lives, whichever is shorter, since the completion of antileukemic therapy (for example, but not limited to, small molecule or cytotoxic/myelosuppressive therapy), with the following exceptions: * Wah-out can be shorter for patients with rapidly progressing disease as determined by the treating investigator * Hydroxyurea for cytoreduction can be initiated without restriction related to timing of study entry. Hydroxyurea can be continued concomitantly with SNDX-5613, with medical monitor approval. Patients may continue to receive prophylactic intrathecal chemotherapy at any time at the treating physician's discretion * Hematopoietic Growth Factors: At least 7 days since the completion of therapy with short-acting hematopoietic growth factors and 14 days with long-acting growth factors * Biologics (e.g., monoclonal antibody therapy): At least 90 days, or 5 half-lives, whichever is shorter, since the completion of therapy with an antineoplastic biologic agent * Steroids: At least 7 days since systemic glucocorticoid therapy, unless receiving physiologic dosing (equivalent to ≤10 mg prednisone daily for patients ≥ 18 years or ≤10 mg/m\^2 /day for patients * Prior treatment with gilteritinib is allowed Exclusion Criteria: * Diagnosis of acute promyelocytic leukemia * Diagnosis of extra-medullary acute myeloid leukemia (AML) based on WHO 2022 classification or myeloid sarcoma * Suspected central nervous system (CNS) involvement. Patients with history of cerebrospinal fluid (CSF) involvement must either have documented CSF clearance prior to treatment initiation or be receiving active treatment for CNS involvement * Participants with prior malignancy, except: * Participants with history of adequately treated malignancy for which no anticancer systemic therapy (namely chemotherapy, radiotherapy or surgery) is ongoing or required during the course of the study * Participants who are receiving adjuvant therapy such as hormone therapy are eligible. However, participants who developed therapy related neoplasms are not eligible * Previous known allergy/sensitivity to components of gilteritinib or SNDX-5613. Prior treatment with gilteritinib is allowed and does not exclude a patient * Patient with known human immunodeficiency virus (HIV) or has active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV). HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. For patients with evidence of chronic HBV infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Individuals with a history of 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 * Fridericia's corrected QT interval (QTcF) \> 450 msec at time of screening * Clinically significant ventricular arrhythmia (e.g., ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) * Uncontrolled intercurrent illness including, but not limited to, unstable angina pectoris, serious cardiac arrhythmia, myocardial infarction within 2 months prior to enrollment, New York Heart Association (NYHA) Class III or IV heart failure * Patients with uncontrolled infection will not be enrolled until infection is treated and under control per the principal investigator or their designee * Any psychiatric illness that prevents patient from informed consent process * Pregnant or breastfeeding at the time of enrollment * Patient has a malabsorption syndrome or other condition that precludes an enteral route of administration * Patient has history of a cardiovascular, endocrinologic, hepatic, immunologic metabolic, neurologic, psychiatric, pulmonary, renal disease, or any other condition that in the opinion of the investigator would adversely affect his/her participation in this study or interpretation of study results