It isn't just FFLs. The Gun Control Act (GCA) defines a list of people who aren't allowed to ship, transport, receive, or possess firearms of ammo. This includes any person "who is an unlawful user of or addicted to any controlled substance (as defined in section 102 of the Controlled Substances Act, codified at 21 U.S.C. § 802);" [1]. Since cannabis is federally illegal still if you use it you can't legally even possess (not just own) a firearm or ammo.
I think it is a stupid law though. Imagine if we applied that logic to other constitutionally protected rights. "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to vote" or "Anyone who is an unlawful user of or addicted to any controlled substance shall not have the right to due process".