We are buying chain link panels and making a run and coop that will be 28' x 7' Over the chain link at one end we are putting three walls. The back wall will be solid and have our nesting boxes open to us from outside the coop and run. The two side walls will have storm shutter style windows that will open to the chain link so air can flow in hot weather. I'm still seriously considering planting a tree in part of this run so roofing may not cover the entire run... however we do want roofing over a large portion of the run and coop for shade. I had thought of the corregated metal for roofing but I'm concerned it will heat the run and coop up too much. My husband suggested we paint it white which I'm sure will help but I'm wondering do any of you have suggestions for other roofing material for such a large run/coop area that will mostly be chain link panels.
A 7' width would allow you to span the top with "cattle panels" attached at either end to the chain link upper bar. Then cover that with either plastic or canvas tarp or nylon shade cloth. The arch, under tension, provides lots of support, with some flex for wind loads. You will need metal wire or bands to make the connection.
Essentially, a "hoop coop" supported at the top of your fencing.
Be aware, however, that doing so will put constant pressure on the top rail, wanting to force it "out" from the center line of your run, while the height off the ground is a lever, magnifying that force down the posts. Use lots of concrete, and an extra foot of burial depth isn't a bad idea. You could also use a tension wire across, though you would then have to dodge it every time you walked thru.
Doing so will give you a height at the center about 6 1/3' above the top rails, making it feel quite roomy in the center. You could also shorten the cattle panels, reducing the arch, but at some point, the arch becomes so shallow that wind or other loads could cause it to invert. I'm not doing those calculations, and not sure the extra labor is worth it, but taking 2-3' length off each cattle panel should be fine based on some back of napkin math. Basically, use some heavy duty zip ties to hold your first panel in place - lots of them - to mock up the final product, then push on it a bunch of times to see how it bows and flexes against a horizontal load.