Whether or not a chicken flies over a fence seems to depends on a number of factors - their size, flying ability, wings clipped or not, and their determination/desperation (what's on their side of the fence vs. the other side).
I had a bantam that could fly >10'. My BA's haven't gotten over a 4' fence to my veggie garden, but if they were more determined maybe they would. It is slim pickins in my summer urban backyard because we don't water the lawn - all the green stuff was in the veggie garden but they didn't get into it. But they are a big breed; a bantam or good flier would be in there in no time. I would advocate trial and error, and when you do your trials, try to keep it cheap and simple. For example you can create a decent chicken barrier with plastic netting, bamboo poles or scrap lumber, and plastic wire ties/string/wire, etc.. Or those cheap green steel fence stakes you can use with chicken wire or welded wire fences. All chickens are different so you should experiment to see what works with yours. I have not had to resort to clipping wings, but I would if needed - something you could consider. Also, try to keep things interesting on their side of the fence - scrap food/compost, scratch, weeds from your garden, an old rotten stump, etc. Good luck!
