The best 3v3 build, to my knowledge, is Toss/Zerg/Terran. I'm in 3v3 masters with a bunch of different teams by just 5-0ing my placements every time. I've even carried gold/plat players to it aswell.
Terran goes gas first, reactor hellion, zerg goes 10 pool speedling, toss 4gates or does ANYTHING, really.
The ling/hell comp will kill any early aggression and you will be able to at least shut down the zerg completely on their team, and maybe even another player. Once they come to counter attack, the protoss is left to macro so theyll have a pretty beefy army to keep you alive. Now you can just expand and macro since you're so far ahead. As the terran I usually just go double armory, pure siegetank/blueflame hellion.
The reason it works is that the speedlings can tank for the hellions, allowing them to splash all over the weak marines/speedlings/zealots of the early game.