Kaido’s ultimate goal is probably the hardest to describe among the Yonkos because of his conflicting reasoning and behaviour.
The thing about Kaido, is that he seems to be tired and bored of life itself, which has resulted in multiple suicide attempts or at least attempts of measuring himself with things that would put a normal human in the ground. Kaido seems almost possessed with the idea of battle and measuring himself with everyone and everything in the world.
Because of this, Kaido’s endgame goal seems to be nothing more than one big war that fuels his lust for destruction and strength that will ultimately be his final act. He will either win this gigantic war against the world, or he will go down fighting and his somewhat tragic tale will come to an end.
Kaido doesn’t seem to have a true intent of becoming Pirate King, but he does show the desire to be the strongest or at least fight with other strong beings. Kaido looks down on the rest of the world (like the Supernovas) and he regards the world as a boring place. This will result in him going to war with the rest of the world. In this sense, he does want to rule the sea, but he isn’t actively looking to become Pirate King it seems, although this isn’t officially confirmed.
Theory by S.