I don't envy you, I encounter a skunk in my chook barn several times this winter/spring in the evenings. Nearly included it in my evening head count of my girls one time! Lol.
I did eventually have to shoot it too, but waited till it was outside the barn. Is there anyway you can leave all the doors open to air out? I don't know what the smell would do to your chickens, but there are products online that claim to neutralize the odor. Just be careful what you use, make sure its safe for chickens to breathe as well.
I also had one get under my house a few weeks ago, it let off a stink bomb at 2.30 am! Everytime the furnace kicked in, up thru the vents in every room! NASTY STUFF! Almost slept in my truck! Smell was pretty much gone within a day or two.
Now I play a battery operated radio every night in the barn, someone told me nocturnal predators do not like to come around where there are sounds of human voices, and so far so good!
Also stopped by a hunting/trapping store and got some fox pee, and I sprinkle a few drops of that around outside of the building for good measure, as I read online they won't hang out anywhere one of their predators might be.
GOOD LUCK! I feel your pain.