just passin by and saw this thread.... I would have suggested mulberries too.
If you were in a warmer climate I might suggest oranges or lemons too. As long as you can protect the drip line from digging from the chickens.
We grow Star Jasmine which is a vine here and has awesome flowers and shade producing foliage. I don't know if it grows in your climate.
Just about any fruit tree would provide shade in the summer. I would pick stone fruit because the seed part isnt easy to swallow. With the exception of cherries. I dont know if cherry pits have any noxious properties.
One thing you can do is use a net below the fruit bearing tree to preserve the fruit that drops for your own table.
Something you can grow for your chickens consumption is Kale.... grow it along side the run they will keep it pruned as far as they can reach then you can trinm it and feed it to them as well.
Just do yourself a favor and check the list of toxic plants there are a few here on BYC.
Some are deadly some are only toxic if eaten in great quantities. but its good to be aware of them all. Regional variations will apply.... some stuff wont grow in cold climates. some stuff wont grow in dry climates
deb