Can chickens fly?

Yes they do and yes they can. 

That said, it depends on breed and how much they wish to escape.

Mine not only fly, they "climb" my 6' fence if they really, really want out (or in.)  I was amazed, have seen it 2 or 3 times now.  They climb with their claws while madly flapping their wings.  Most days they calmly stay in this yard -- it has to be something unusual to bring this on.

Up to you.  Many on here put a top on to keep hawks out -- or if it's strong enough, to keep most anything out.  I would imagine most breeds will stay inside a 6' fence most of the time; it will vary with the breed.  You may want at least part of it covered anyway to keep snow out.

Mine fly all the time.  They've flown on top of my shoulder while I was standing in their coop.  They fly to the top of the run all the time.  I do have a top on the run as well.  I don't want them escaping nor do I want other birds flying in there and snatching up my girls.

Yes. And not only the flying/climbing out, but predators from land and air can easily get in. After learning the hard way, ALL my runs are covered with wire or a roof.

Every now in then my five do the quail flush, straight up into the wire above, ten feet high. Yes chickens can fly, not very good but they can fly

FYI, I am going to tell you what an old-timer told me, chickens are fun, but remember, everything wants to eat them.

That very intresting but do your pets want to???

Sometimes.The Black Sumatra and the Sicilian Buttercup,are known to be more flighty than other chickens.Still, there are some heavy breeds that can barely get off the ground,making them a better choice for some people.Of course, you can stop birds from being flighty if you clip their wings.