Joe, human physiology and canine physiology are entirely different to rat physiology. Here's what we know. If you feed a rat a diet of bromate, pure bromate, not parts per thousand, parts per million or parts per billion, 100% bromate, the rat will get cancer. If you owned a pet rat or a mouse, I might advise you not to feed it a diet of pure bromate
But then I'd also advise you not to feed it a diet of pure salt, pure nutmeg, pure baking powder or pure anything. Almost every ingredient becomes dangerous when you consume it in large enough quantities, even water.
Without even knowing if bromate is a human or canine carcinogen, the parts per million in the flour become no more dangerous than the parts per billion in the baked crust. Does this mean that I eat raw pizza dough or feed it to pets? Of course not, but a scrap of dough that makes it to the floor is going to be harmless. Not that scraps of dough really should ever be making it to the floor. I don't know about your household, but I find drops of chocolate ice cream on the floor all the time. Peas, raisins, anything round and small, the ground is like a magnet. But dough? I've made at least 500 pizzas at home and never once did dough end up on the floor. Depending on how vigorously I toss a pizza, I might get a very light dusting of flour on the floor, but, at most we're talking half a teaspoon, and to get that much in total, the dog would have to lick a pretty large section of floor. I know dog biscuits are usually flour based, but do dogs even enjoy the taste of raw flour?
Unlike bromate, chocolate is a well documented danger to dogs. Is your home chocolate free? If it isn't, are you careful with it? A bromated flour NY style pizza is way better than chocolate
I sincerely don't think you need to be that paranoid, but if you really can't get past this phantom fear, then just be as careful with the bromated flour as you are with chocolate. If you're conscientious, the dogs are never going to eat dough or anything close to a meaningful amount of flour.