Mill
Any fabric used for acoustic sound panels has to meet the following criteria:
Flammability meets ASTM-E84, Class A; California Bulletin 117; and NFPA 701.
It must be acoustically transparent, and generally, it is 100% polyester. Some of the fabrics have Olefin and Acrylic fibres along with the poly, but some of these don't meet NFPA 701. If the fabric is glued to the panel, the flammability rating is lower than if it is stretched over batt insulation.
A good fabric will have high resistance to stretching. Some fabric manufacturers we have used are Tandem Fabrics Inc., Victor, and Guilford of Maine. Whoever does the installation will have access to a variety of fabrics which meet the specifications.