You can certainly plant something in the run for shade/cover, but you will have to fence around it for at least a year to give the root system a chance to get established. Things like blackberry, raspberry, grapevine, or blueberry bushes make great cover, and they also provide some forage for the flock.
Keeping vegitation in your run. - Page 2
Featured Stories on BackYard Chickens
My chickens are able to free range daily for about the last two hours of the day during my work week, and then on my days off they are out most of the day, so long as they don't venture far enough to find our veggies. They really enjoy the horse pastures and breaking up the manure.
You can plant mulitfloral rose but if you do the SWAT team may pay you a visit and make you dig it up. There is nothing more invasive except maybe Small Pox. Let it get a good start because even though multifloral rose will stop a T-Rex, I am unsure if it will survive chickens. All I can say is mine did.
Lilacs are a good one!
I'll add Rose of Sharon because the leaves and flowers are safe and rich in calcium.
I've got one on my run surrounded by wire, which I'll remove when it is tall enough. They'll strip the base, of course.
They can get quite tall, depending on the species, but are easily pruned.
We have ferns, daffodils,hydrangea, tulips and rhododendrons all over the property, all of which are toxic to chickens, however we have never had a problem with them eating any of those plants. As a matter of fact, every so often we get a rogue hen who decides she needs to perch in our rhododendrons and make them her home. And we have to pack her up and take her back to the hen house at nights. All three years, with completely different hatches and blood lines we have the same issue with the rhododendrons.