Anti Alergenic fly spray. In Australia its sold in the tall blue can, with the little list of circles down the side with all the tiny creepy crawlies it kills, kills it fastest. Blast up against the grain of the scales so it goes underneath those raised edges.
There is no circle on the can for mites, but it works brilliantly, the anti alergenic is ok on their scales, (and your skin if you aim badly).
Later to speed the slough-off and regrowth process, regular moisturize with Lanolin does wonders, or Sorbalene at a pinch, if your desperately trying to get a rough spot cleaned up regrown in time for show season. You can pick off the rough dead stuff physically to help them shed the damadged area quicker. Give into that scab picking inner child? Certainly anything lumped up unnaturally in a horrendous infestation you can cut off before you even start to treat them. Otherwise, a week after treatment start exfoliating the rough spots off.
To be certain redone the treatment every second day 3 times, the breeding cycle is 3 daily, so this should get everything, but honestly one properly applied can treatment does the job.
Old breeder taught me years ago, the look of the can has changed a few times but it's still available. Highly gentle, highly antialergenic. A two second blast and you are done, not mucking around pasting on oil or vaseline or yellow legs or similar.
If you want the trad poultry keepers "secret" Yellow Legs Ointment mixture:
Sulfer and Kerosene - mix to a crumbly toothpaste consistency.
Lard, melt slightly and pour in slow, mixing until the whole lot is a proper toothpaste consistency.
Lard is your carrier agent, you want as little as possible, just enough to make it sticky enough to put on gloves and slather it on chicken legs, and the bedding sticks to it instantly.
Sulfur and Kero is the actual treatment.
Various other additions by breeders, but basic secret Yellow Leg Ointment for hundreds of years is simply that. I never saw the point of the secrecy, withholding things that would help birds fight disease and problems!
Cooking oil or Vaseline work too, just take longer, and need more applications, as they don't kill the eggs, they rely on cutting off oxygen on the adults, and it doesn't stay on unscuffed very long, whereas Yellow Leg Ointment is virulent stuff, reeks, sticks, if mixed well, and kills all developmental forms of scaly leg.
A few bites of it wont kill the chook either, and I've tried switching out Lard (the bit they want to taste sample) for part Sorbelene, to varying degrees of effect, or little added vaseline for extra 'stick' with the sorbaline.
Good luck!
I'd also say add spray your hen houses and perches when the birds are not in them, then get some Diatomaceous Earth sprinkled into your yards, laying boxes, perches, etc, as its microscopically fine razors within make it delightful for chooks (aussie word for chickens) to dust bath in and express new feathers, they adore it, and those microscopic bits in its white powder get in and chop up scaly leg mites and feather lice and their eggs, which really lowers your birds chances of getting infected, even if freeloading bin chickens(ibis) visit your yard, or bloody pigeons and wild cockies (parrots) regularly cascade lice down onto your chooks from above!
Ongoing management commitments mean retopping up their Diatomaceous Earth monthly ideally, but a big bag from a feed store will last you a while being sprinkled.
Hope this helps and give you a better understanding of the 'why' of some of these things.
All the best
Dr Alicia Manolas
Perth, Western Australia