Flanagan played college football at Purdue University from 1962 to 1964. Flanagan grew from 190 pounds to 230 pounds between his freshman and sophomore year. During his sophomore and junior years, he played center on offense and linebacker on defense. As a senior, he was the starting center for the 1964 Purdue Boilermakers football team that featured Bob Griese at quarterback and compiled a 6–3 record and finished in third place in the Big Ten Conference. Flanagan was selected by the conference coaches for the United Press International as the second-team center on the 1964 All-Big Ten Conference football team. He also played in the Blue-Gray Game and the Senior Bowl after his senior year.