Technically they COULD have wings, because Maiar are able to physically manifest themselves any way that they want. Balrogs don't have wings in the books, but they do in movies thanks to good ol' Ralph.
If a Balrog hadeth wings it would have flappethed them when it felleth witheth Gandalf and watchedeth as Gandalf felleth to his death. While flappething its wingetheths. And snickeringethedeth.