Briere has two goals and an assist during his three-game points streak.
The Coyotes may have No. 1 goaltender Sean Burke back in the nets Sunday. Burke activated from injured reserve Friday after missing 19 games with a sprained knee. He sat on the bench that night at Dallas as Brian Boucher made 31 saves.
The Flames have recorded just one victory in their last 11 games (1-7-3-1). The stretch began with a 4-3 loss in Phoenix on January 28 and most recently, the Flames dropped a 4-1 decision at Nashville on Thursday.
The Flames surrendered three goals in the first nine minutes on January 23 and suffered a 7-1 home loss to the Coyotes.
Phoenix has 16 wins in its last 21 meetings with Calgary.