Inclusion Criteria:  Provision of signed and dated informed consent form Stated willingness to comply with all study procedures and availability for the duration of the study Eastern Cooperative Oncology Group (ECOG) performance status ≤2 FLT3-ITD or FLT3-TKD mutated AML (non-M3) in 1st or greater relapse or refractory to at least one prior line of AML directed therapy FLT3 testing must be confirmed at the time of disease relapse Adequate organ function Left ventricular ejection fraction (LVEF) ≥50% Prior anthracycline exposure ≤368 mg/m2 daunorubicin (or equivalent) Ability to take oral medication and willingness to adhere to the medication regimen For females of reproductive potential: use of highly effective contraception including double barrier methods (condoms with spermicidal jelly or foam and diaphragm with spermicidal jelly or foam), oral, depo provera, or injectable contraceptives, intrauterine devices and tubal ligation. For females of reproductive potential: negative serum or urine pregnancy test with a sensitivity of at least 50mIU/mL within 10 days and again within 24 hours of beginning study treatment For males of reproductive potential: use of condoms Breastfeeding mothers must agree to discontinue nursing  Exclusion Criteria:  Patients may not be receiving any other investigational agents Patients with documented central nervous system involvement of AML Any prior use of gilteritinib Patients must not have evidence of GI tract abnormalities that would alter the absorption of oral medications Major surgery within two weeks of first dose of study drug. Patients must have recovered from the effects of any surgery performed greater than two weeks prior WBC count ≥50,000 at the time study treatment begins. Use of hydroxyurea to maintain WBC <50,000 is allowed up to the time that study treatment begins Predicted inability to tolerate standard induction chemotherapy Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements No other malignancies in addition to AML that are currently requiring treatment with the exception of: 1) basal cell or squamous cell carcinoma or the skin; 2) carcinoma in situ of the cervix or breast; 3) a history of breast cancer that is currently being managed with adjuvant endocrine therapy Patients may not have undergone an allogeneic stem cell transplant at any time in the past