Flaman, a rugged defenseman from Dysart, Saskatchewan, was signed by the Boston Bruins in 1943 and had one-game NHL cameos in 1944-45 and 1945-46 before becoming a regular midway through the 1946-47 season, just after turning 20. He helped anchor Boston's defense until being traded to the Toronto Maple Leafs on Nov. 16, 1950.

The move to the Maple Leafs put Flaman on a team that had won the Stanley Cup three times in the previous four seasons. He fit in perfectly, playing an integral role on defense and helping the Maple Leafs defeat the Bruins and Montreal Canadiens en route to Toronto's fourth championship in five seasons.

Toronto traded Flaman back to Boston on July 20, 1954, and he played some of the best hockey of his NHL career in his final seven seasons with the Bruins. He was named a Second Team NHL All-Star three times (1954-55, 1956-57 and 1957-58) and finished in the top five in Norris Trophy voting for five straight seasons between 1954-55 and 1958-59. He had his best offensive season in 1956-57 with 31 points (six goals, 25 assists) in 68 games. He also took on a leadership role, spending his final six seasons with the Bruins as captain.

His NHL career ended after the 1960-61 season, but Flaman was named player/coach of Providence of the American Hockey League and spent three seasons in that role before retiring as a player in 1964.

In 911 NHL games, he had 208 points (34 goals, 174 assists). He also had 1,370 penalty minutes, third-most in NHL history at the time. He played in the NHL All-Star Game six times.

Flaman spent one more season as coach of Providence, moved on to Fort Worth of the Central Hockey League and then spent the 1969-70 season as a scout for the Bruins where he assessed college prospects in the Northeast. That led to his next job, coach of Northeastern University, in 1970. He held that post for 19 seasons, the longest tenure in Northeastern history. He guided Northeastern to the program's first four Beanpot Tournament championships, was named NCAA hockey coach of the year in 1982, when Northeastern advanced to the NCAA Frozen Four, and coached the Huskies to the Hockey East championship in 1988.

He left the school after the 1988-89 season and became a scout for the New Jersey Devils.

Flaman was inducted into the Hockey Hall of Fame in 1990. He was 85 when he died on June 22, 2012.