The Calgary Flames selected Kulak, a defenseman born in Stony Plain, Alberta, in the fourth round (No. 105) of the 2012 NHL Draft after his first full season with Vancouver of the Western Hockey League. He spent two more seasons with Vancouver and had 60 points (14 goals, 46 assists) in 2013-14 before signing a three-year, entry-level contract with the Flames on March 18, 2014.
Kulak started his first pro season in the ECHL, was promoted to Adirondack of the American Hockey League and made his NHL debut on April 11, 2015, in Calgary's season finale. Kulak spent most of 2015-16 in the AHL, playing eight games with the Flames, and earned 21 games with Calgary in 2016-17, earning his first NHL point with an assist on Oct. 18, 2016.