You can *pick up* flamethrowers in campaign, Not zombies, You trade out of a chest.
Also in multiplayer the only way for this to happen that I know of is that someone had a lvl 65 account with the flamethrower equiped as a perk, Then someone from Treyarch reset his/her account to level one, But they still have the perks on.
Thanks
Please click the egg,
Luffs
~Zy