The Flyers sent a conditional second-round draft pick previously acquired from the Florida Panthers and a fourth-round pick in 2013 to the Lightning for the 34-year-old Czech.
Kubina was held out of Thursday's game against San Jose as the team sought to trade him and was scratched again for Saturday's game against Washington.
Over 52 games this season, Kubina has three goals and eight assists along with 59 penalty minutes.
Since breaking into the league with the Lightning during the 1997-98 season, the former seventh round draft pick has totaled 110 goals and 272 assists in 953 games with the Lightning, Thrashers and Maple Leafs.
He was named to the All-Star team in the 2003-04 season and won the Stanley Cup that year with the Lightning.
Kalinski, 24, was selected by the Flyers in the sixth round of the 2007 draft and had nine goals and three assists for in 40 games this season for the AHL's Adirondack Phantoms. He appeared in 22 games for the Flyers from 2008-10, recording a goal and four assists.