Your reference to "weasels and bats" might mean you're in the northern hemisphere with winter coming on. Where I am (the Australian New England) such sounds are usually made by birds looking for nest sites in spring, so my comments may be irrelevant.

In my experience the flapping has been caused by wings against the inside of the flue and the bird can't get out at all unless you detach the flue from the wall, far enough for it to "fall" out of the lower end of the flue. This can be tricky and it can be even trickier to reattach the flue properly. A cap of chicken wire over the top of the flue after your last fire will keep birds (and weasels or bats) out, and won't impede flue gases much if you forget it and light your first winter fire with it in place.

Cheers, Rowan