Permethrin is just the synthetic version of pyrethrin, a naturally occurring compound from marigolds.
Buy permethrin concentrate. Buy a garden sprayer, mix the concentrate to the amount indicated for treating livestock and buildings. Clean the coop really well. Everywhere, including nooks and crannies. Excluded birds and spray everything including roosts (top and bottom).
Next, with a helper if available, spray the birds, focusing on the vents, legs, under wings, between legs. Put into coop as they are sprayed. Repeat entire process in about 7 days.
Try to exclude wild birds bc wild birds bring in pests and disease such as mites, lice, avian influenza. So if wild birds are nesting in the chicken area or sharing the chicken pellets, you should try to exclude them from the coop and feed areas at a minimum. Even if you free range, keeping the coop and feed areas free of wild birds will help.