Nah, the main antagonist always goes down last. Kaido is not going to fall before King, that's patently absurd.
This is an unconventional arc. For starters, Zoro is on the roof with Luffy.
King has too much going for him to be second fiddled. And coincidentally, in the same arc Zoro (according to outside sources) also has a mysterious past.
The theme of this arc from the enemies perspective is when the chips are down, Pirates will always leave your side. I would like to see where K/Q/J go after Kaido falls or is in danger of dying. That's why I expect King to go after Zoro if and when ZKK happens. Bc that's what I would expect Zoro to do if Luffy was in danger/dying.
And expecting Sanji to fight King is absurd.
How can Sanji come out of this arc YC1+ and then go to face Burgess or someone who isn't YC1? Especially given his background of having no fights and being stopped by a haki-less Doflamingo/Vergo? Unless the raid suit is a Yonko level Powerup.
I'm not 100% in this prediction, after a possible Kaido FB, it will be more defined.