If you mean say 3/4" thick: 1) Why use it? and 2) it won't work as well as thinner plywood or, as was pointed out, siding which is really plywood but not that thick.Well, will a thick plywood work? I can't get solid wood due to how much I have to spend.
I hope you are not thinking of this as a box with one piece of plywood nailed to another. No matter how small it is, focus on the frame. Then whatever siding you use is atached to the frame but not to other pieces of siding.
You haven't said how big the coop will be, but with reasonable framing, usually 2x4's, 1/2" should be thick enough for the siding and 3/8" might be OK. (You'll see ridiculous numbers like 11/32 and 19/32 thick. It's sort of like "pounds" of coffee which now come in 12-ounce bags. Usually you can add 1 to the first number so 11/32 becomes 12/32 and then it's just immediately obvious (right!!) that it's 6/16 or 3/8 thick. Well, almost. 1/32 inch less than 3/8. 19/32 is (almost) 5/8 inch.)
See https://www.google.com/search?q=t1-11
I wouldn't worry about painting the inside but if you do, anything you'd use in your bedroom should be good enough for the chickens. Formaldehyde won't be a problem. You're going to have to have ventilation (unbelievable stink if you don't) and that will take care of it.
PS: Just noticed where you live. I lived there many years and loved it.
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