A Study of CPX-351 (Vyxeos™) With Quizartinib for the Treatment of FLT3-ITD Mutation-Positive Acute Myeloid Leukemia

Inclusion Criteria: 1. Written informed consent form (ICF), according to local guidelines, signed by the patient or by a legal guardian prior to the performance of any study-related screening procedures. 2. Patients with the following types of AML with \>5% blasts: * Relapsed FLT3-ITD mutation-positive AML, diagnosed by bone marrow (BM) biopsy with FLT3 mutation by polymerase chain reaction (PCR) * Refractory FLT3-ITD mutation-positive AML, diagnosed by BM biopsy with FLT3 mutation by PCR * Relapsed or refractory FLT3-ITD mutation-positive AML after HCT, diagnosed by BM biopsy with FLT3 mutation by PCR * Relapsed or refractory AML with de novo FLT3-ITD mutation, diagnosed by BM biopsy with FLT3 mutation by PCR * Relapsed or refractory AML after HCT with de novo FLT3-ITD mutation, diagnosed by BM biopsy with FLT3 mutation by PCR 3. First-line therapy must have contained a standard induction chemotherapy (e.g. 7+3, FLAG-IDA, FLAG, CLAG, MEC, hypomethylating agent with venetoclax) with or without receiving a prior FLT3 inhibitor (e.g. midostaurin) or multi-tyrosine kinase inhibitor (e.g. sorafenib). All patients who relapsed after an alloHCT are included, except patients with active graft-versus-host disease (GVHD) requiring \>10 mg prednisone. 4. Patients must be able to swallow and retain oral medication. 5. Eastern Cooperative Oncology Group (ECOG) Performance Status score of 0, 1, or 2 (Appendix A). 6. Adequate renal and hepatic parameters (aspartate aminotransferase \[AST\], alanine aminotransferase \[ALT\] ≤2.5 institutional upper limit of normal \[ULN\]; total bilirubin ≤2.0 institutional ULN; serum creatinine \[Cr\] ≤2.0). In patients with suspected liver infiltration, ALT can be ≤5 institutional ULN. Exclusion Criteria: 1. Acute promyelocytic leukemia (t\[15;17\]) 2. Female patients who are lactating or have a positive serum pregnancy test during the screening period. Female patients of childbearing potential who are not willing to employ highly effective birth control (as defined in Appendix C of protocol) from screening to 6 months following the last dose of CPX-351 and/or quizartinib. 3. Evidence of active and uncontrolled bacterial, fungal, parasitic, or viral infection. Infections are considered controlled if appropriate therapy has been instituted and, at the time of screening, no signs of active infection progression are present. This is assessed by the site clinicians, including an infectious disease consulting physician, if requested by the Principal Investigator (PI), regarding adequacy of therapy. These infections include, but are not limited to: * Known human immunodeficiency virus (HIV) infection * Active hepatitis B or C infection with rising transaminase values * Active tuberculosis infection 4. History of hypersensitivity to cytarabine, daunorubicin, or an FLT3 inhibitor 5. Any patients with known significant impairment in gastrointestinal (GI) function or GI disease that my significantly alter the absorption of quizartinib. 6. Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol. 7. Uncontrolled or significant cardiovascular disease, including any of the following: * Bradycardia of less than 50 beats per minute, unless the patient has a pacemaker * QTcF interval using Fridericia's correction factor (QTcF) interval prolongation, defined as \>450msec at screening and prior to first administration of quizartinib * Diagnosis of or suspicion of long QT syndrome (including family history of long QT syndrome) * Systolic blood pressure ≥180 mmHg or diastolic blood pressure ≥110 mmHg * History of clinically relevant ventricular arrhythmias (i.e., ventricular tachycardia, ventricular fibrillation or Torsades de pointes) * History of second or third degree heart block without a pacemaker * Right bundle branch and left anterior hemiblock (bifascicular block), complete left bundle branch block * Ejection fraction \<50% by transthoracic echocardiogram (TTE) or multigated acquisition (MUGA) scan * History of uncontrolled angina pectoris or myocardial infarction within 6 months prior to Screening 8. History of New York Heart Association Class 3 or 4 heart failure 9. Prior anthracycline (or equivalent) cumulative exposure ≥368 mg/m2 daunorubicin (or equivalent) 10. Any serious underlying medical condition that, in the opinion of the Investigator or Medical Monitor, would impair the ability to receive or tolerate the planned treatment. 11. Patients with inadequate adequate pulmonary function will be excluded. Inadequate pulmonary function is defined as requiring supplemental O2, or diffusing capacity of the lungs for carbon monoxide \[DLCO\] \<40%. 12. Active acute or chronic GVHD requiring prednisone \>10 mg or equivalent.