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.
Professional football
Flanagan was selected by the Detroit Lions in the fifth round, 64th overall pick, of the 1965 NFL Draft. His initial contract with the Lions was for a $2,000 bonus and $12,000 a year. While playing for the Lions, Flanagan supplemented his income in the off-season selling steel to the automobile companies, selling real estate, and working for a beer distributorship owned by former Detroit Tigers star Vic Wertz. Flanagan took over as the Lions' starting center as a rookie in 1965 and held the position for the next ten years. From 1965 to 1974, he started 139 games for the Lions, including a streak of 129 consecutive games. He was selected to play in the Pro Bowl four times, in 1969, 1970, 1971 and 1973. He was also selected by the UPI as a second-team All-NFL player in 1969 and by the Pro Football Writers as a second-team All-NFL player in 1970. Flanagan developed a rivalry with Chicago Bears linebacker Dick Butkus. Flanagan recalled Butkus as his "greatest challenge." He was quoted in 1973 calling Butkus "a wild man on defense... one of the most foul-mouthed guys in the league... he insults you, your mother, and the team." Flanagan also claimed that Butkus "would spit down the back of his neck." In May 1975, Flanagan signed with the San Diego Chargers. At the time, he said he was "happy to be back home in my native state," but emphasized that he had been treated well by the Lions and was leaving under "happy circumstances." He was the Chargers' starting center in the 1975 and 1976 seasons. In July 1977, Flanagan was traded by the Chargers to the Los Angeles Rams. However, he was released on waivers by the Rams in early September 1977 prior to the start of the regular season.
