Born in Vermilion, Alberta, Flett played his minor hockey in Okotoks, Alberta, then played junior hockey with the Melville Millionaires of the SJHL. From 1963–64 through 1966–67, he played for teams in various minor professional leagues. In 1967, when the NHL expanded from six to twelve teams, Flett was drafted by the expansion Los Angeles Kings. In his rookie season, playing on right wing, he scored 26 goals and was named The Sporting NewsNHL West Divisionrookie of the year. Flett was nicknamed "Cowboy" because in addition to being a hockey player, he owned a cattle ranch in Alberta and he was also a rodeo performer. Flett's rodeo career ended when the Los Angeles Kings owner Jack Kent Cooke threatened to fine him $1,000 for every rodeo he appeared in. He was well known throughout his career for being one of the few hockey players at the time to sport a full beard, and for being one of the last players to play without a helmet. Not known for his playmaking skill or skating, Flett did possess a booming and heavy slapshot and when paired with the right center who could get him the puck, he was among the league's biggest scoring threats. Flett scored 24 goals in his sophomore season. His goal production declined significantly in his next two seasons. Fed up with his dwindling production, the Kings traded Flett, along with Eddie Joyal and Ross Lonsberry to the Philadelphia Flyers where he had his best season in 1972–73 with 43 goals. Flett was a member of the Flyers 1974 Stanley Cup champion team. After the season ended, he was traded to the Toronto Maple Leafs where he reverted to his indifferent play, and as a result, the Leafs put him on waivers. The Atlanta Flames picked him from waivers, and Flett had one last productive year in the NHL when he scored 23 goals in 1975–76. In 1976–77, the Flames sold him to the Edmonton Oilers of the WHA where he averaged over 60 points per season over the next three years. When Edmonton joined the NHL, he found he had little left and retired after 20 games. He scouted for the Oilers after that.
Death
In May 1999, Flett entered the hospital due to a gall bladder condition which eventually contributed to liver failure. Flett received a liver transplant; however, his body rejected the transplant. Flett died on July 12, 1999 due to liver failure. He had battled alcoholism for many years and claimed to be sober for "4 or 5 years" after checking into the Betty Ford Clinic in Rancho Mirage in the early 1990s. Flett was survived by his wife Doreen and three sons, Cody, Dean and Shane.