Here is how doubles/singles works in other fighting games:
A team consists of two or three players. They send out one first vs another one. The winning player is still in, the losing player is out. In a lot of cases, regardless of who wins, both sit out the next match, and new players compete in the next match.
For example:
Inui/Atomsk/Izumi vs Keitaro/Eazy/Yes
Atomsk goes in first, takes out Yes.
Next match is Inui vs Keitaro, Keitaro takes out Inui.
Next match is Izumi vs Eazy, Izumi beats Eazy.
Keitaro faces Atomsk, loses, and the match is over.
Inui/Atomsk/Izumi win with two players left.
Step it up.