This study will evaluate two doses of Quizartinib in patients with relapsed or refractory acute myeloid leukemia who are also FMS-like tyrosine kinase - internal tandem duplication ( FLT3-ITD) positive. Patient will be randomly assigned in a 1:1 ratio to one of two treatment arms. Both treatment arms will receive Quizartinib but at different doses. The study treatment is taken orally in 28 day cycles until either disease progression occurs or an unacceptable toxicity occurs. In addition to the study assessments to evaluate the disease, blood will be drawn to measure drug levels and biomarkers. Patients will be followed for survival at three month intervals after the end of treatment.