I used an rubberized roof coat product I got from Lowes. (Blackjack#57) It comes in a 5gal bucket. It's made to handle all kinds of weather extremes on a roof, so protecting a chicken coop floor is nothing to this stuff. It's been down over two years on my coop's floor, and when I clean out the coop, it looks as good as when I first put it down. With a big floor like you are going to have, this is the way to go. Just open the bucket, STIR well, dump it out on the floor and push/apply it with a paint roller. It totally seals all the floor seams, plus the gap where the walls meet the floor. Unlike vinyl or linoleum, this stuff becomes a permanent part of the floor so nothing can get under it. Linoleum over time will break down in a coop and start deteriorating. Then you have to go back and redo it. Not a big problem in a small coop, but a headache in a big one.
Jack