I think you might be forgetting something about Blaziken, it is based off a bird(true...) However; Said bird is a chicken and well... Chickens don't fly.
Actually, they can. They're just too fat/heavy for extended flight periods. So they can definitely fly up into a tree, but not to the next house down the street.
Actually, I worked on a farm that raised chickens and no, they can't fly. It is gliding if it is not sustainable. Sure they can get a extra lift with the wings but saying that is flying is a little farfetch'd(see what I did there.)