I'm still early in the game (just got Sharla) but I think I am missing something with the chain attacks, because they don't seem to be anything special except for popping off some emergency heals (I'm probably doing something wrong, will backtrack in this thread for info).
Also, does anyone else have issues changing targets when there's more than two? I've been playing as Reyn because the AI doesn't seem to be able to tank competently but sometimes when one of the other members pulls aggro I can't seem to switch my target to the loose mob... even if the mob is positioned in front of me it sometimes feels like the targeting system jams up or something or outright refuses to target the mob in front of me.
Awesome game though, it has pulled me away from ME3.
The chain attacks have several uses. Best thing is that it resets all cooldowns, which helps with the emergency heals you talked about. You can also reliably topple / daze an enemy. Finally, if you use multiple abilities of the same color in sequence they get stronger.
Also, when you have attacked with all characters, you might get a b button prompt. Time it right and you'll get another attack in. The higher the affinity between your party members, the higher the chance that you'll get the prompt. Later on in the game a chain attack can easily consist of 6+ attacks.