Well, lots of non birds have wings and there are even birds that have things that can only generally be called "wings" (penguins, emus) so developing wings would not suggest at least to me "bird". However the term vertebrate does imply something that has a backbone.
There is no classification I know of that is "things that fly" comparable to the classification vertebrate and invertebrate.
Anyone so limited that they can only spell a word one way is severely handicapped!