DR Elmore, we’ve had a similar concern with Poe off and on since he was a kitten. He’s nearly 16 now and we still have to guard against leaving certain types of things lying around. Our vet explained way back then that he’d seen “pica cats” (which was my introduction to that meaning of the word), and that Poe seemed to be one.
Do your best to rid yourself of the flaking paint. That’s easy to say; doing so might be difficult or impossible. But also just mention it to his vet next time you’re talking to them. Not sure there’s anything much you can do about it. In our case, it’s certain kinds of plastic that are attractive to Poe, and he (thank God) threw up a bunch of it once which scared the bejesus out of me.