All chickens produce a lot of dust from their feathers which is essentially dried up specks of skin. They fall off the base of the new feathers as they grow in.
New feathers are constantly growing individually to replace those that fall out here and there, but during a moult when a lot of feathers are falling out and regrowing at the same time, the amount is dust produced is significantly more. All hens have a minor moult after each brood.
The only thing to help remove the dry skin is dust bathing. Otherwise it's best to just leave it alone.
Skin flakes and specks from feather growth will be white and easily fall off, whereas 'dust' that clings in clumps at the base of the feathers and looks more greyish could be mites.