Well, the Balrogs were Ainur. So if you could conclusively prove that they had wings, then you could conclusively prove that Ainur had wings.
However, to bypass that, let's go straight to Thorondor and the Eagles of Manwe, who are said in Tolkien's later works that they must have been Maiar (aka lesser Ainur) in origin.
But it boils down to this fact:
Wings are a physical part of a body. The body of any Ainu depends on his choice (or, more likely in the Balrogs' cases, on the choice of the person they obey unquestioningly). Hence, it varies from Ainu to Ainu, a fact that is further complicated by the fact that a great number of the Ainur could change forms or not wear any at all.
Therefore, it follows logically, that there is no one general statement to be made, and must be evaluated on an Ainu-by-Ainu basis.