No wings. 'Like' wings is exactly what is described, although there is obviously confusion in some people's minds when the later phrase mentions 'its wings'. But that is all it is - a moment of confusion and ambiguity. Once you read the text again, it is clear that Balrogs do not have wings.
As simple as that.
However, I always imagined them having wings because of all the illustrations and models of them in that state. And they do look soooo good with them, as evidenced by PJ's version in the films. So, although I know that Balrogs didn't actually have wings, I don't mind seeing them portrayed with them.