Safety and Efficacy of Quizartinib in Children and Young Adults With Acute Myeloid Leukemia (AML), a Cancer of the Blood

Inclusion Criteria: Participants must meet all of the following criteria to be eligible for enrollment into the study: * Has diagnosis of AML according to the World Health Organization (WHO) 2008 classification with ≥5% blasts in bone marrow, with or without extramedullary disease * In first relapse or refractory to first-line high-dose chemotherapy with no more than 1 attempt (1 to 2 cycles of induction chemotherapy) at remission induction - prior HSCT is permitted * Has presence of the FLT3-ITD activating mutation in bone marrow or peripheral blood as defined in the protocol * Is between 1 month and 21 years of age at the time the Informed Consent/Assent form is signed * Has protocol-defined adequate performance status score * Has fully recovered from the acute clinically significant toxicity effects of all prior chemotherapy, immunotherapy, or radiotherapy, per protocol guidelines * Has protocol-defined adequate renal, hepatic and cardiac functions * If of reproductive potential, is permanently sterile or agrees to use highly effective birth control upon enrollment, during the period of therapy, and for 6 months following the last dose of quizartinib, etoposide, fludarabine, methotrexate, or cytarabine, whichever is later * If female of child-bearing potential, tests negative for pregnancy and agrees not to breast feed * Male participants must be surgically sterile or willing to use highly effective birth control during the treatment period, and for 6 months following the last dose of quizartinib, etoposide, fludarabine, methotrexate, or cytarabine, whichever is later. * Participant/legal representative is capable of understanding the investigational nature of the study, potential risks, and benefits, and the patient (and/or legal representative) signs a written assent/informed consent Exclusion Criteria: Participants who meet any of the following criteria will be disqualified from entering the study: * Has been diagnosed with isolated central nervous system relapse, acute promyelocytic leukemia (APL), juvenile myelomonocytic leukemia, French-American-British classification M3 or WHO classification of APL with translocation, or with myeloid proliferations related to Down syndrome * Has uncontrolled or pre-defined significant cardiovascular disease as detailed in the protocol * Has systemic fungal, bacterial, viral or other infection that is exhibiting ongoing signs/symptoms related to the infection without improvement despite appropriate antibiotics or other treatment. The patient must be off vasopressors and have negative blood cultures for at least 48 hours prior to the start of systematic protocol therapy. * Has known active clinically relevant liver disease (e.g., active hepatitis B or active hepatitis C) * Has known history of human immunodeficiency virus (HIV) * Has history of hypersensitivity to any of the study medications or their excipients * Is receiving or is anticipated to receive concomitant chemotherapy, radiation, or immunotherapy other than as specified in the protocol * Has any significant concurrent disease, illness, psychiatric disorder or social issue that would compromise subject safety or compliance, interfere with consent/assent, study participation, follow up, or interpretation of study results * Is currently participating in another investigative interventional procedure (observational or long-term interventional follow-up is allowed) * Is otherwise considered inappropriate for the study by the Investigator