Our dog yard and the chicken run share a fence and after one of my hens and my Roo went flying over I added some fence around the top to make it taller. I just used some chicken wire and some small rods and added a few feet. Haven't had that problem again. Ended up doing it all around the whole chicken yard. Works great to keep them from flying over since I don't have a top to my run..It's just a fenced in area where all the coops are in.
I did the exact same thing. The problem for me is that the ramp out of the coop borders the fencing so I think if they get on the ramp they can get a bit higher and fly over. I need to raise the fence up even more with some chicken wire. It sounds like we have very similar set ups.