Fleischer received his PhD from Princeton University in 1982. After leaving Princeton, Fleischer held teaching posts at Washington University in St. Louis and the Ohio State University. The MacArthur Fellows Program awarded Fleischer what is colloquially knows as its genius grant in 1988, which is "a five-year grant to individuals who show exceptional creativity in their work and the prospect for still more in the future". In 1993, Fleischer joined the faculty of the University of Chicago. Fleischer focuses primarily on Ottoman history, specializing in the Age of Süleyman. Currently he is developing on a major work on Süleyman the Lawgiver while utilizing a number of papers dealing with the time period. He also works on apocalypticism and its relationship to his field of study. Fleischer also sits on the editorial board of a number of publications, including Cambridge Studies in Early Modern History and International Journal of Middle East Studies. Fleischer is also a former director of the University of Chicago's Center for Middle Eastern Studies and a member of the editorial board of Historians of the Ottoman Empire.