Not sure why you want a skylight instead of installing the plexiglass in the wall as a window. I have some concerns you might be creating a greenhouse that will cook you chickens with that plexiglass in the direct sun. You could easily have ventilation issues. If you are counting on folding the back wall down for ventilation, are you sure you will always be around and available to make that adjustment when required. I find the best designs are the ones that require minimum adjustment and care.
A flat roof will leak unless you are very careful. Even if it doesn't leak, water could pond on it, rotting or rusting it out. I think you would be better off sloping the roof so the runoff goes away from the coop and run. A skylight in a flat roof will make the leaking and ponding worse.
Parts of eastern Kansas gets enough rainfall to support trees, so rain and the roof leaking is a concern. I know you normally don't get real deep snows and coops of this size can easily have pretty strong roofs with just a little support, but make sure the roof will support the heaviest snow you will occasionally get. You should be looking at the unusual year for the design load, not the normal year.
With coops this size, make sure you consider how you are going to clean them out. You don't have much room to get in there and work.
There are advantages and disadvantages of having the coop floor on the ground. Purely personal preference.
Others can probably come up with a cheaper method of roofing it, but I'd consider a sloping roof, covered with plywood, then topped with metal roofing material from Craigslist. The metal will likely have old nail holes in it, so you would need to seal those. With coops this size, that should be doable. You could probably get asphalt shingles from Craigslist also.
