Does the flank strap force a bronc to buck?

No, although a tight strap around the flank can make a horse buck and kick to try and get rid of it. The flank strap on a bronc (or bull) is actually fitted pretty loosely, with just enough pressure to let the animal know it is there.

It is a training signal to tell the horse it is time to start bucking now - broncs are horses with a job the same as ordinary saddle horses, and is released by the wranglers once the horse is no longer needed to buck.

A ranch (saddle) bronc at Dubois Rodeo.