There is an argument for and against wings:
"The Balrog reached the bridge. Gandalf stood in the middle of the span, leaning on the staff in his left hand, but in his other hand Glamdring gleamed, cold and white. His enemy halted again, facing him, and the shadow about it reached out like two vast wings. It raised the whip, and the thongs whined and cracked. Fire came from its nostrils. But Gandalf stood firm."
(The Lord of the Rings)
This shows that the Balrog only had things which looked like wings, not actually having wings itself.
Here is something saying the opposite:
"It stepped forward slowly on to the bridge, and suddenly it drew itself up to a great height, and its wings were spread from wall to wall; but still Gandalf could be seen, glimmering in the gloom; he seemed small, and altogether alone: grey and bent, like a wizened tree before the onset of a storm."
(Lord of the Rings)
You will notice it doesn't say LIKE in this quote, therefore it does imly that it had wings. However this is becuase Tolkien has already said 'LIKE wings' in the previous quote so there was no need to do it again.
In my view Balrogs may have had things which looked like wings, but were made out of the shadow surrounding the body of the balrog, not the actual body itself. Therefore it could not use the Wings to fly.
Even if it did have wings it is highly unlikely that they could fly becuase all the known Balrogs were [u]killed by falling from a height[/u]. If they could fly they could stabalise themselves.
(Ecthelion killed and got killed by Gothmog, Glorfindel killed and got killed by another balrog, Gandalf killed and got killed by Durins bane).
Plus a small point even if the could fly (which they couldn't) it is doubtful they were ever fly away from the enemies.