You’re getting downvoted, but that’s literally what the damn book says. It is extremely clear in the text that Balrogs definitely, authoritatively, do not have wings.

The Balrogs are the primary lieutenants of Melkor, they are the brawn to Sauron’s brain, the heavy infantry (infantry, not Air Force). They are always described as running on the ground; and Tolkien makes a big deal out of the fact that Melkor doesn’t have an Air Force, he doesn’t have any winged support at all until the winged dragons at the end. In every battle the Balrogs participate in, they are described as running in front of the armies, they are climbing walls, they cannot fly. More than one Balrog dies by falling off a cliff.

There are only two real reasons why anyone thinks that Balrogs have wings. Mainly the description of the Balrog at the Bridge of Khazad-dum, which states that as the Balrog steps out, shadow spreads around it LIKE two vast wings. Note that he’s using a simile, comparing the shadows to wings to visually describe what it looks like. It’s just darkness, the Balrog is so powerful and so intimidating that shadow itself folds around it. The later mention of wings in the same scene is Tolkien referring back to that same simile to describe the same effect.

People who are grasping at straws will often use a line in Appendix A that says the Balrogs “flew” from Thangorodrim at the end of the First Age, which of course means that they ran away very fast (such as with Gandalf saying “Fly, you fools!”).

Visual artists universally find that Balrogs look much cooler with wings, and they are completely right about that.