Your correct it's vinyl. But at .66¢ a sqft, it's not very expensive. The only downside is it's a 12' wide roll, so if coop isn't 12' wide, your going to have some waste, or a seam. I used some of my extra to line my nest boxes and poop boards.
Home Depot or Lowe's still has it on bulk rolls.
If your still in the planning stage, build the floor and then install the linoleum to the edge. The bottom plate of the wall covers the edge so it can't curl.