dunno if this would be practical, but:
if you could find the remains of a roll of aluminum flashing, you'd probably need it AT LEAST 12" wide and wider would really be better, wrap it all the way around your run NEAR THE TOP of the run walls. you can punch holes nr the edge of it and use bits of wire or zip-ties. The idea is that the squirrel climbs up the run fence but then can't get a hold for the last little ways to get over the top.
Might be a problem in high winds. But I've seen vaguely similar things done to keep other climbing crittrs out, so I thought I's at least mention it.
You need to train your chickens somehow to go after squirrels. Hm, catch a squirrel, dip him in peanutbutter and roll him in scratch, then set him loose, maybe the chickens will then think *all* squirrels are made of candy... LOL
Good luck, they are frustrating little buggers aren't they,
Pat, who just discovered fresh rabbit tracks in the garden, snarl