Tubby is all black, and has had dandruff is whole life. When I first took him to the vet for it years ago, he suggested I feed him a "premium" food such as Science Diet. Seems the "premium" foods have more fats in them than the store bought ones. That didn't work for Tubby, so the vet gave me some oily stuff to put on his food. That didn't work either, so the vet said don't worry about it, he has dandruff. I could bath him, but I'm kind of attached to my limbs and would hate to loose them.

If it's not the parasite thing, and just dandruff, I really wouldn't worry about it.