If it's a chainlink kennel, they are great but you may want to make sure the wire is fully secured at the bottom so something cannot push thru. If you have fuzzybutts, you will need to run a tighted weave wire or netting along the bottom and in the corners to keep them in. If you can, skirt the outside to keep diggers out. A alturnate to digging in skirt is to attach it to the fence panel and lay it out flat about 18 inches and even pin or weight it down. Diggers start at the base of the fence and if they cannot get thru the wire, they usually move on. If your coop is secure, a tarp roof will work. If not them you will need to cover it with wire to keep coon out. The neat thing about chain link is you can cut tree branches a little longer than the run is wide and hang additional roosts or perches outside for a hot day perch in the shade.
As for a coop, a crate with a lift off top for cleaning and egg collection with couple milkcrates to lay in works great and is all you need. A inside roost is important however if you don't have one just cover the milk crates as they will perch on them
PS. If you elevate the coop so the birds can go under it, you won't loose run space