What you see as peeling "paint" is what is called "seasoning" - which smoke and other particles coat the metal. That is good and you want that to adhere to the walls of the smoker. You don't want it to build up too much, too the point it becomes flakey and falls off onto your food. When you start to see it build up to the point it becomes bubbly, and/or flakey, crumble up a sheet of foil into a loose ball, and use that to rub of any seasoning that looks loose or bubbly.
Now to the second part of your problem - why is it falling off. It is not normal, but it does happen. There may be other causes but this is what causes mine to peel off, when it does happens to me on rare occasions; it is because I smoke/roast too many chicken wings at once. Chicken with skin produces a lot of moisture inside the cabinet, too much moisture inside the cabinet; besides keeping the temperature down and producing "black rain", it will soften the seasoning and it will begin to blister (bubble), and peel off down to the metal.
I would use a crumbled up foil and rub loose any seasoning. Next do a dry run; no smoke or water bowl, heat the Bradley to 250°F, and run it for a couple of hours. Once the cabinet has cooled, use the crumbled up foil one more time to rub off any loose seasoning. Then proceed to season your smoker like you did when you first got it.
Keeping the vent open wide enough to let excess moisture to be expelled, my resolve your problem.
