A flyer is "a person or thing that flies," and the last time I checked birds fly. A red wing is "a small migratory thrush that breeds mainly in northern Europe, with red underwings showing in flight." I was unaware that this quiz has already been done.
With all fairness, I did extensive research after the first comment and learned that the Philadelphia Flyers was meant to be vague, describing the way the players "fly" around the ice. I still don't know the intent of the Red Wings name, but a redwing is a bird regardless, so I still think that it should be included on this quiz.
I didn't miss the Anaheim Ducks, and as I said before, redwings are a type of bird, so the intent of the name really doesn't matter in the context of this quiz.