Fleming attended the University of Florida in Gainesville, Florida, where he played for coach Bob Woodruff's Florida Gators football team from 1956 to 1958. Fleming was the Gators' team captain in 1958, and he finished his college football career as a first-team All-Southeastern Conference selection. Woodruff ranked him as the Gators' best receiver of the 1950s. The Chicago Cardinals drafted Fleming following his senior football season, but he chose to remain in school and exhaust his remaining NCAA baseball eligibility playing for coach Dave Fuller's Florida Gators baseball team from 1958 to 1960. He was the captain of the Gators baseball team, and led the Gators in home runs and stolen bases.
Professional career
Fleming was selected by the Chicago Cardinals in the 28th round of the 1959 NFL Draft, but he remained at the University of Florida and did not play during the NFL season. He successfully urged Chicago management to trade him to the Cleveland Browns before the start of the season. Fleming was a close friend of another Browns defensive back, Bernie Parrish, a fellow Florida graduate, and the two were said to be almost inseparable during the NFL season. Over the following three years, Fleming played regularly at safety, intercepted ten passes, recovered four fumbles, and made The Sporting News All-NFL team in.
Fleming, his wife Rosalie and their son Ty lived in his hometown of Shadyside, Ohio, during football season, and in Winter Park, Florida, during the NFL off-season. As a 25-year-old NFL All-Conference selection, Fleming was already planning for when his professional football career ended. He had majored in building construction at the University of Florida, and had been working as a foreman for a Central Florida construction company during the off-season to stay in shape and gain industry experience. On June 4, 1963, Fleming and a co-worker, Walter Smith, were operating a crane on a construction site west of Orlando, Florida, when the boom of the crane brushed an overhead 12,000-volt high-tension electrical transmission line. Fleming and Smith were electrocuted, and attempts to revive them at the hospital failed. Earlier the same day, the Browns had announced that Fleming had signed his contract for the 1963 season. His death came only 17 days after that of Ernie Davis, the overall No. 1 pick in the 1962 NFL Draft, whom the Browns had acquired in a trade. The Browns retired both Davis' uniform number No. 45 and Fleming's No. 46 in memory of the players. Fleming Field at Shadyside High School, Fleming's alma mater, is named in his memory. When the Browns practiced at Western Reserve Eclectic Institute, the field house they used also carried Fleming's name. Fleming was nominated for the Florida Sports Hall of Fame within days of his death, and he was later inducted into the University of Florida Athletic Hall of Fame as a "Gator Great."