At the age of eight, Fleming hopped on a freight train to Chicago to escape his abusive father. Following hospitalization for gang fight injuries, he returned to California where he lived with his mother and worked at Paramount as a laborer. Fleming joined the Merchant Marine, and then he served in the U.S. Navy in the Pacific in WW II, where he was a Master Carpenter in the Seabees.

From 1946 to 1957, Fleming appeared on stage in Chicago and New York with featured roles in numerous plays on Broadway including "My Three Angels," "Stalag 17," and "No Time For Sergeants." Fleming's television career began in the early 1950's with live performances on "Hallmark Summer Theatre," "The Web," "Suspense," "Kraft Television Theatre," and many other dramatic series. In 1954, he starred in Paramount's film "Conquest of Space," followed by "Queen of Outer Space" for Allied Artists. In 1958, Fleming became the star of CBS-TV's long-running western "Rawhide" as the trail boss Gil Favor. He remained with the top-rated show for seven of its eight seasons, and he had planned to retire to Hawaii where he had purchased a ranch.

He acted in "The Glass Bottom Boat" in 1965, and he was hired by MGM-TV to film the two-part adventure program "High Jungle" in Peru. During the shooting of location shots on the Huallaga River on September 28, 1966, Fleming dove (intentionally?) from a dug-out canoe after paddling it beyond the rapids. His body was lost in the turbulent water and was not recovered until three days later.