Kylington, 25, played 73 games last season, totalling nine goals, 22 assists and a plus-34 rating.
The native of Stockholm, Sweden, has played 168 games over five seasons with the Flames after the team selected him 60th overall in the 2015 NHL Draft.
Kylington is coming off a one-year deal worth $750,000. He will be an unrestricted free agent when his next contract expires in 2024.
The two sides were scheduled to go to arbitration on Aug. 10.