Yes, it would help to know what zone you're in, but here's some info. for the time being...
There's a safe plant list here:
https://www.backyardchickens.com/a/safe-plants Though that doesn't mean the chickens won't eat them. If you want to prevent them from being eaten, as was stated, it would be advisable to surround the bottoms of them with hardware cloth so that the chickens can't get to them.
I've been pondering the same thing though. I was thinking about doing Nasturtiums and Black Eyed Susan vines to cover the outside of the run, but they're annuals and I was wanting a perennial in case I didn't have time to fool with replanting (as I don't know how well these plants resow/reseed themselves...I'm still gonna give it a try and see though...if they do that's great, as I heard that Nasturtium can be good eating for us, as it adds a peppery taste to salads...sounds yummy!). I was thinking as far as a perennial, I may do a climbing rose on the outside of the run to cover it, make it pretty and provide shade, but would need one that could take the heat here in western KY, is resistant to black spot and I would like a rebloomer. I'm still searching through types for that. Right now I have my eyes on the Star roses and plants/Condard-Pyle website. They have the Knock Out Rose, which is the only rose I've got that hasn't been ravaged by black spot (out of my other roses, one has a little, one I'm battling it with, and another succumbed to it). There's a gorgeous white rose on that website that I really like...it looks much like an English rose. It's called Cloud 10 (Rosa 'Radclean'). 3 1/2" diameter blooms, very vigorous vegetation, a loose climber, 7-8 ft. tall and 5 ft. wide, abundant and continuous flowering, resistant to black spot and excellent for rust and mildew. Sounds like the rose for me! Here's the website if you want to check it out:
http://www.conard-pyle.com/index.cfm/fuseaction/home.home/index.htm
As far as inside the run, I was thinking of doing a butterfly bush. Many do not get more than 6 ft. tall with a 4-6 spread, so that sounds great, as my run is 6 ft. tall. The ones that appealed to me most was the BiColor, Purple Emperor, Royal Red, and Nahano Purple. I think I like the BiColor the best. They usually bloom from July - Sept. and the ones I picked grow fast and are widely adaptable in terms of moisture. I got the info on them from this site (and there are more to chose from than what I listed):
http://www.naturehills.com/bushes-and-shrubs/butterfly-bushes?limit=36 I would surround the bush with hardware cloth so that the chickens couldn't get to it.
Anyway, these are just my thoughts on what I'm thinking of doing, as, like I said, we don't know what zone you're in.
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