Such a beautiful set-up. It is looking so alive and well!
Your shade cloth doesn't look too bad. I use one in my fruit orchard for my chickens.
As for your run, since it is opened to the top, shade might be a bit hard. You could get a big Beach umbrella that you can open on sunny hot days and retract on cooler cloudy days. Normally I always suggest a run to have a fencing top to it because a daytime Owl strike or a Red-tailed Hawk could come along. Nothing worse than an unexpected visit from a predator.
I have a run that is covered with fencing, and the vine I chose to apply to it was Honeysuckle. It grows so well, so fast, and it feeds and attracts hummingbirds. I also like that it smells so heavenly which can mask any chicken odors that can occur over time.
My flight used to be completely open to the sun, but now it is covered so that it is completely shade 24/7. My chickens do have access into the open orchard for full sun, but I still provide a shade cloth for their protection.
Here is the flight about 3-4 seasons ago. The Honeysuckle is just getting to the top. I did have a crab-plum that I planted inside of the flight and in the next picture you will see it also growing up through to provide shade.
Here is the flight this morning (do not judge the weedfulness!) What a ton of growth!
In years to come, as the plum tree expands its canopy across the top of the flight, I will begin to slowly remove most of the vine growth. It likely will begin to fail anyways once the tree overtakes it all. So this might be your answer. What about a tree in the run? A fruit tree or nut tree would provide them with some goodies too each year.
Here is where I utilized my shadecloth. Also, that is Buck my rooster and Dharma the Mottled Cochin.
Remember, chickens are so very humble, even a cardboard box is a thing of luxury!
Ron
You should be a shamed of yourself. 
wifezilla are grapes picky or hard to grow? I'd plant some too if I could get 25 lbs of grapes!!
