check your local ordinances first, even though a bb gun doesn't do much damage, if someone saw you shooting with one in an area where shooting is prohibitted or shooting the cats is illegal you could still have legal issues even though it is only a bb gun. I doubt if your chickens ate a bb it would hurt them, bb gun bbs aren't lead. I would start by calling the police or animal control, whichever is in charge in your area, it is likely allowing straying cats or dogs is illegal and the owners will at a minimum get a good talking to and possibly a fine, I have even heard of owners being arrested for allowing straying animals, it also may be legal to kill them whether or not they are doing damage, it may be legal to shoot them only if they are attacking your birds or you. Either way check your local laws and do as you see fit, I have dog issues and start with the sheriff's dept who will issue a ticket if they catch the dogs running loose on my property, this doesn't do any good because the owner is a vile, sad excuse of a human being so my next step is to wait til the dogs do damage and kill them which is legal here. Having complaints on record works in your favor legally and may solve the issue altogether.