Fiberglass is an inorganic material, and as such, is a noncombustible insulation material that is not flammable. The main issue that arises is that many people will apply vapor retardant to the surface, and the vapor retardants that are commonly used are flammable.
To avoid the flammability of vapor retardants, it is a good idea to use gypsum board or another approved facing material to finish the installation. Since fiberglass insulation is not combustible, there is no need to apply flame retardants to it after installation. The noncombustible nature of fiberglass insulation lasts for the entire life of the insulation material.