There is no text that anyone's aware of which describes balrogs as having wings (so there's nothing saying "and then the balrog flapped its wings and flew away" or whatever). But there are bits of texts which can be interpreted in various ways, and these meanings can be 'added together' to come to the conclusion that balrogs were winged or weren't. The problem is, in some cases, the one piece of text can be interpreted either way.
Anyhow, I'm certainly no expert on balrogs. For some more informed opinions, you should probably look in the articles section of
www.barrowdowns.com.