Yeah, you will need a lot of ventilation. In Georgia cold is not your enemy, heat is, but it can still get below freezing. You’ll need ventilation in the winter but summer is when it gets dangerous. You are far enough south that you will get a lot of weather influence off the gulf coast.
Don’t worry about keeping them warm in winter, with their down coats that can manage that for themselves. Where you are they’d be fine sleeping in trees in the winter from a weather standpoint. In trees they’d be able to move around and get out of direct winds, so just ventilate your coop to avoid breezes on them in the winter. In summer, breezes hitting them will feel good.
How much shade will that coop be in? Will it be exposed to the south and west sun, the hot sides? My coop has a metal roof and the west side is metal, the rest wood. It does not get too hot. I have a lot of ventilation and no insulation. With enough ventilation you don’t need insulation. When cutting your vents, I suggest lots up high but also a decent sized vent down low. In the summer you want cooler air coming in to push hot air out up above. The cooler the air coming in the better that works. So cut your low vent on the north or maybe east side where it stays in the shade. That air will be a lot cooler than if you cut the vent on the sunny side.
Do not put your nests on the south or west sides where they can become an oven in the sun. Positioning the roosts is less important because the coop will cool off when the sun goes down, but maybe put them a bit further from the wall if they are on the west side. But if you can I’d suggest the nests and low vent on the north side with roosts on the east.
Condensation will form on that metal on many mornings. It can seem like it’s raining inside some mornings from my metal roof. It hasn’t created any problems for me, with my ventilation and the bedding on my dirt floor it dries out soon enough, but it can cause problems for some people. If you insulate anything in that coop it would be the roof to stop that condensation. With enough ventilation you don’t need insulation to protect against heat.
I don’t understand what you mean by wrapping that chain link under the shed. Could you elaborate a bit?
How big will your run be, width x length? How tall is your chain link fence? You need to be able to walk in there without hitting your head. Wire can get expensive. The heavier the gauge and the smaller the mesh, the more protection it adds but the more expensive it is. 2” x 4” welded wire fencing will stop practically any decent sized predators and isn’t all that expensive but some things can still get through. I don’t know how big the openings on your chain link fencing are either, so matching that size will give you equivalent protection.
I don’t know if you need to support that top to keep it from sagging but hog rings usually work well to attach fencing to fencing.