Where are they coming from? If they are that bad, there must be a source of standing water nearby that is breeding them. Otherwise they should be dispersing somewhat or the chickens are hanging out a lot in the coop and the skeeters are staying in their for a full buffet. I'd look around for sources of standing water first since they will die out if they aren't continually being replenished.
If you start spraying insecticides around, you're risking getting it on the chickens, in the feed etc. Have you considered getting a mosquito zapper and setting it AWAY from the area to draw them away from the coop to their death? Is the coop screened?
I would go with more natural things like spraying orange oil solution or citronella in the coop while the chickens were locked out of it and then letting it air out and dry before letting them back in. Or perhaps hanging citronella repellant devices inside the coop.
The biggest thing is prevention and finding the stagnant water source where they are laying mosquito eggs. Using mosquito dunks when you can't empty out the water source (such as a pond, rainwater collection barrels, etc) is very helpful.
ETA: permethrins are great insecticides but they are neurotoxic and tiny amounts will kill cats and dogs are also susceptible to poisoning when coming into contact with permethrin if the dose is too high.