Kraft received a degree in Biochemistry from Brown University and his M.D. from the Stanford University School of Medicine. He completed the Harvard combined residency in Internal Medicine and Pediatrics at the Massachusetts General Hospital and the Boston Children's Hospital, before returning to Stanford for clinical fellowship training in hematology/oncology and bone marrow transplantation and a post-doctoral fellowship with Dr. Irving Weissman, and was subsequently on Stanford faculty on clinical faculty with the UCSF pediatric bone marrow transplantation service at University of California, San Francisco (UCSF). Kraft has peer-reviewed scientific publications which include in Science and Nature.