How often did you use the permethrin? Mites are deadly since they cause anemia, and they cannbe very hard to completely get rid of. Certain ones will stay on the chickens 24/7 while another type will feed on them at night and hide in the coops cracks during daylight. Mites hatch out every 3-7 days, so you need to treat the chickens 2-3 times at 7 day intervals, so the newly hatched ones do not reproduce. Permethrin won’t kill mite eggs, only the live ones. Also the bedding must be hauled away and the coop, nest boxes, ams roosts should be sprayed with permethrin spray. It lasts about 30 days. Permethrin dust is better for cold temperatures, and the spray can be used about 1 tablespoonful per chicken in warmer weather. Elector PSP is supposed to be a very good treatment as well. I would not bother with DE for a mite infestation, and it can affect lungs and eyes of bith the chickens and people.
Ivermectin can be used. The 5 mg per ml pour-on such as Ivomec or the generic dosage is 0.1 ml per every 2 pounds, placed on the back of the chicken over the spine. Then repeat in 14 days. I am not sure of the oral type of ivermectin dosage, but it could be used. It is available as horse wormer paste.
There are other methods of coop treatment, including white washing, neem oil, and sulfur powder. But the permethrin spray, which also comes in permethrin 10 concentrate, and is mixed with water is one of the least expensive and effective.