Did you read it? Explicitly says they have wings.

He says they have wings. As I said, if you want to take that they are made of shadows you can, but they have wings.

I can’t believe people still argue over whether or not Balrogs have wings when the text unambiguously says they do. You can have wings and also have a shadow that looks like wings.

His enemy halted again, facing him, and the shadow about it reached out like two vast wings.

...suddenly it drew itself up to a great height, and its wings were spread from wall to wall...

Like two vast wings but then he explicitly says its wings were spread, clearly stating it has wings. To be the most generous you could try to say the wings are made of shadows, but based on the text they’re clearly still wings.

Yes, Balrogs have wings.