Yes the choke in a shotgun will definetly make a differance in your ability to hit flying targets. Typical chokes that come with a shotgun are cylinder, improved cylinder, modified, and full. And then there are chokes that fall in between and around those with regards to the ammount of constriction they have.

The more open a choke the larger pattern it will produce. The more constricted the choke the tighter the pattern will be.

Say you are hunting low and flast flying doves. You would want a fairly open choke such as a skeet or improved cylinder. If you are hunting decoying ducks where shots wild be a little farther out then you may want to choose a slightly tighter choke such as a modified or improved modified. If you are hunting passing geese then you may want a full choke.

Basically the farther out the target the tighter the choke you want to use in your gun. The faster the target is moving and/ or the closer it is the more open you would want the choke.