This was written mainly for Northern Fowl Mites, adjust timing/frequency of coop treatment vs. bird treatment for Red Mites if needed, as they primarily live in the coop and feed at night)
For the coop - Clear out all the bedding. Burn it or otherwise bag up and dispose of it. Spray all surfaces (though I skipped the ceiling and top parts of wall though, because my coop peak is too tall) and crevices with liquid permethrin, including roost bars and nests. After it all dries, put in new bedding (I made sure to do my spraying early in the day, so it was mostly dry by late afternoon so the chickens could go back in).
For the chickens - Dust with permethrin powder or spray with liquid under belly, under wings, on back, around base of neck, around vent. If they're getting them on their heads (which you may see scabbing around comb or even eyes if it's bad), I'd carefully pat some around the base of the comb or just behind the head, but I wouldn't spray them directly in the face.
You'll need to treat again in around 7 to 10-ish days, as permethrin doesn't kill eggs. Recheck in another 7-10 days and if needed, treat again (but if it's a light or moderate infestation, that shouldn't be necessary).