Fleming's debut came in 1969, when he competed at Talladega. It was a solid start for the young driver, starting 20th and completing most of the race to garner a 14th place finish, one that would prove to be his career-best.
Fleming's other two races waited until the 1974 season to happen, starting off at Bristol. Despite a late engine problem there, Fleming managed to record a solid 15th place finish. Unfortunately, he couldn't rise above a DNF at Martinsville either, finishing dead last (30th) after another engine issue.