Kylington, a native of Stockholm, Sweden, was chosen by the Calgary Flames in the second round (No. 60) of the 2015 NHL Draft.

Kylington grew up in Sundbyberg, just north of Stockholm, playing hockey, soccer and floorball. But the demands of practices and an injury playing soccer made him choose one sport, hockey.

"My dad has been a big supporter for me in my hockey," Kylington told NHL.com on March 26, 2015. "He didn't play hockey when he was little; just for fun. He played handball. He had a bit of a passion for hockey and when I was little I tried out some sports like soccer, hockey and floorball. I liked hockey and soccer. When I got to an age I chose hockey and I stuck to it."

Kylington, a defenseman, made his Swedish Hockey League at age 16 with Farjestad in 2013-14 and was loaned to AIK of HockeyAllsvenskan, Sweden's second-highest league, the following season. He returned to Farjestad and was among the top 10 European skaters eligible for the 2015 draft.

Kylington signed a three-year contract with the Flames on July 15, 2015. He remained in North American and was assigned to Stockton of the American Hockey League. He made his NHL debut against the Minnesota Wild on April 9, 2016, before playing the next two seasons with Stockton.

Kylington signed a one-year contract with the Colorado Avalanche on Aug. 5, 2024. He returned to the NHL on Jan. 25 after not playing in 2022-23 to attend to his mental health. He was a finalist for the Masterton Trophy, given annually to the NHL player who best exemplifies the qualities of perseverance, sportsmanship and dedication to hockey as voted on by members of the Professional Hockey Writers Association. Arizona Coyotes goalie Connor Ingram won the award.