A flash suppressor assembly that captures, burns, and cools the combustion gases produced when a projectile, such as a bullet, is fired by a weapon. The flash suppressor assembly includes a housing with an internal space containing a tubular burn chamber disposed about a burn tube that define at least one set of an accelerated gas flow chamber, an expanded burn chamber, and an elongated cooling chamber. The outer surface profile of the burn tube includes grooves that facilitate the intermixing of oxygen with the combustion gases to enhance burning thereof.