I have to agree with both Tom and Sidechain... Wood frames will improve the appearance of your panels.. much tighter look. To "test" a fabric, I wrap some around my head. If you can't hear any attentuation of the high freq, then the fabric is acoustically transparent. If the HF sounds attenuated, then the fabric is going to reflect some HF. Avoid backed fabrics....
The flamability of glue could be an issue should (heaven forbid) and insurance claim be required.... as could the flame spread rating of the fabric itself. This is one the key reasons (discussed at our acoustics panel at TOC this week) to use a 'known' quantity in the fabric. Guilford FR701 (the basic standard) is about $16-17 per linear yard which is 66" wide... not cheap, but not expensive.
You can go and buy fabric at any local fabric store that is acoustically transparent, but there is the flame spread issue. If you are concerned about the possible insurance ramifications look for Class A ASTM Flame spread rating.