Kulak will be assigned to the AHL Laval Rocket.
The 24-year-old cleared waivers on Monday, and had two goals and six assists in 71 games with the Flames last season.
Valiev heads to the Flames organization after finishing 2017-18 with the Canadiens, playing in just two games after being acquired from Toronto.
The 23-year-old has appeared in 12 NHL games in his career.
Taormina, 31, had four goals and 52 points in 63 games with Laval last season.
He won the Eddie Shore Award as the AHL’s top defenceman in 2016-17.