Born in Cleveland on November 27, 1928, Fleischman was encouraged to study architecture by an uncle who noticed his avid interest in drawing and building models. During his senior year at East Tech High School, Fleischman won a scholastic scholarship to Carnegie Tech (now part of Carnegie-Mellon University). After finishing a five-year program, he spent two years at Columbia University followed by a one-year traveling fellowship that allowed him to visit historic sites in Italy, Spain, Greece, Germany and Scandinavia.

During his illustrious career, Richard completed nearly 500 projects and earned 280 awards, including the Cleveland Arts Prize (1974).