He got away with the "wings" because he had taken flying training in the early days of aviation. I believe it was when he was First Lord of the Admiralty in WWI. I can't remember now where I read all this, but he was prevailed on to give it up in light of his senior ministerial office, and because his instructor, an officer of the RN, wrote himself off in a crash.
Incidentally, I was told many years ago by a senior officer that Churchill was the man who actually created "wings". As told to me, he had just got back from a trip to France, where he had bought a Napoleonic "Eagle" brooch as a gift for Mrs Churchill. He was in discussion with Captain Murray Sueter, and the topic of a special badge for pilots came up. "Something like this"? he said, and held the eagle against Sueter's sleeve. And so it befell.