The only SMGs with multiple elements are the Chulain and the Florentine.
Chulain is always slag, but has a chance to spawn with shock as well. It is a quest reward for the final Clan War mission - side with the Zafords. Just dashboard or sign out if you don't get the one you want, and try again. (main game).
Florentine is always shock and slag and is sold by the seraph vendor in Flamerock Refuge in the TTAoDK DLC.
Other elemental SMG legendaries (all in the main game):
Hellfire (fire) - dropped by Scorch in Frostburn Canyon. Fire DoT has high chance to proc and will stack multiple times for massive fire DoT.
B**ch (any element or no element) - dropped by BNK-3R. High accuracy and crit damage bonus.
Slaga (slag) - dropped by Tector Hodunk in the Dust after completing the Clan War on the Zaford side. High chance to slag and fires 3 projectiles per round.
Baby Maker (any element or none) - dropped by Madame Von Bartlesby in Tundra Express or Mad Dog in Lynchwood. Tediore reload produces a second "baby" SMG when it explodes, which also explodes. --- (Im)mature Aussie gamer. Don't pay the ferry man. Don't even fix a price. GT: Charon78