@Rosalinda,
yes. it is polyester. and "microfiber" is simply a fine (or low) denier polyester
if it is inherently flame proof it comes from Hoescht or BASF, if it is topically treated the fire retardant can come from several sources.
i sell fire retardants for polyester. usually the back surface is coated with a mix of the fire retardant and a latex rubber. to pass a commercial flame retardant standard you general must pass the NFPA 701 VERTICAL STANDARD. as of yet there is no residential flame retardant standard.