Ok I wonder if this is how things will play out:
Zoro fights Queen, and Marco fights King. Zoro and Marco are victorious. Luffy and Zoro reach the top at the same time. They realize that both Big Mom and Kaido are there. Zoro fights Kaido and Luffy fights Big Mom. Big Mom gets defeated by Luffy but Zoro can't deal enough damage on Kaido to be victorious. Then everyone (of the Samurai Alliance) starts attacking Kaido eventually defeating him.
King will survive as Luffy or the Strawhats never have killed someone who was the last of their race. Since Yamato keeps whatever Kaido's heritage alive in him I feel that Kaido dying would make sense.
Anyways that's all I've got for now. Can't wait for the scans/tracings to come in!