I got a concentrated permethrin from the feed store. It has mix instructions for spraying poultry, but you will have to calculate the tiny amount for a spray bottle because the instructions are designed for large commercial poultry farms. I mix it into a spray bottle I have set aside specifically for spraying chickens. (I got my spray bottle from the feed store but you could use a good plant mister. Just mark it so you don't accidentally use it on plants.)
It is easier if you spray the birds at night on their roosts. Don't spray on the top of their feathers. You need to get the spray down to the skin. While the birds are roosting, I pick up their tails and spray under the fluff under the vents. (You don't want to spray directly on the vent.) I also spray under each wing, and I move the feathers aside to get a couple of other squirts onto their sides near the tail.
When the infestation is really bad I will dip the chickens. For dipping I halve the concentration recommended because they get more liquid on them when dipped and you can over-dose them. Mix the dip with warm (not hot) water in a five gallon bucket, or whatever is large enough to dunk your bird with room to spare. Hold the bird by the head and the thighs and dunk, keeping the head OUT of the dip. Swish them around a little so the water gets down to the skin. Let them drain off but don't rinse them. Make sure they have a warm place to dry off. (I only dip them on warm days, preferably in the high 70's or above.) Dipping is a drastic procedure. Once I got the infestation under control I have not had to do it again. But dipping did get the bad infestation under control. Now the occasional spray treatment is all I need to do.
I also switched their feed to Nutrena's "Feather Fixer." That has helped.
Roosters tend to get lice and mites before the hens do. And some birds are more prone to the bugs than others. It is not unusual to have a couple of birds in a coop with bugs, and no significant bug load on the other birds. One of my poultry mentors told me roosters have a slightly lower body temperature than the hens, so the bugs will attack the roosters first.
Avoid eating the eggs for a couple of weeks after spraying the birds with permethrin. And don't spray chickens you plan to eat in the next few months.
Never had peafowl or turkeys so I don't know how they react to sprays. Personally I avoid Ivermectin because I eat my chickens and Ivermectin scares me even more than Permethrin does.
Can't recommend Feather Fixer enough. It has not stopped the bugs completely, but I haven't had a major infestation since I started using it.
Good luck.
