AFAIK, if you can breathe through it, you're good. Now, bass trapping in particular is less restricting with fabrics, because bass waves will pass a lot of things, but not necessarily for the higher freq's. IOW, if you want to absorb high frequencies, you might want to do further research on what really is more transparent. Sometimes, people want it to be more "live", and actually don't want to absorb HF.
Burlap, silk, batik, cotton are some fabrics that should work.
Here's some polyester, Guilford of Maine FR701
http://www.acousticsfirst.com/guilfrd1.htm
more options
http://www.acousticalsolutions.com/products/fabrics/index.asp
yet more options
http://www.acoustex.com/Home.html
some DIY kits, or they'll charge you $20 if you want to give them your fabric of choice for them to build with, I think
http://www.readyacoustics.com/index.php?main_page=index&cPath=26_11_15
going to be the most expensive for sure, but can look great. send a pic to them, and they'll do it for you.
http://www.gikacoustics.com/gik_artpanel.html
if DIY, you're going to want to use DIY, like Ritz, because paint is reflective.
