Oh man. I saw the title and was just drawn in, knowing a controvery was brewing
I don't think Balrogs had wings. I think the whole "shadows like wings" bit in FotR is just a metaphor for the shadow of dark power that the Balrog put out. And if they did have wings, why wouldn't the Balrog in Moria be able to fly out of the cavern under the Bridge of Khazad-Dûm? Plus, I believe I read somewhere that at one point Trolls traveled with the Balrogs, and Trolls certainly can't fly. The only thing I am sure of is that the Balrogs couldn't fly, wings or no, but I personally don't think they had wings anyway.