A Study of Gilteritinib (ASP2215) Combined With Chemotherapy in Children, Adolescents and Young Adults With FMS-like Tyrosine Kinase 3 (FLT3)/Internal Tandem Duplication (ITD) Positive Relapsed or Refractory Acute Myeloid Leukemia (AML)

Inclusion Criteria: * Subject is aged ≥ 6 months and \< 21 years of age\* at the time of signing informed consent and/or assent, as applicable. * \*For phase 2: Enrollment of subjects from 6 months to less than 1 year and 1 year to less than 2 years will be dependent on the establishment of recommended phase 2 dose (RP2D) in the respective age groups during phase 1. * Subject has a diagnosis of acute myeloid leukemia (AML) according to The French-American-British (FAB) classification with ≥ 5% blasts in the bone marrow, with or without extramedullary disease (except subjects with active central nervous system \[CNS\] leukemia). * In the phase 1 portion of the study, subject must be in first or greater relapse or refractory to induction therapy with no more than 1 attempt at remission induction (up to 2 induction cycles). * For the phase 2 portion of the study, subject must be in refractory to or at the first hematologic relapse after first-line remission induction AML therapy (up to 2 induction cycles). * Subject has fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study. * Myelosuppressive chemotherapy: * For subject who relapses while receiving cytotoxic therapy, at least 21 days must have elapsed since the completion of cytotoxic therapy and prior to screening, unless the subject has recovered earlier than 21 days. * Cytoreduction with the following can be initiated and contin…