According to the lastest chapter, Kaido and Big Mom plan to find the Ancient Weapons and the One Piece.
Kaido also plans to move his base to the Flower Capital and transform Wano into a pirate nation with Yamato as shogun. He calls it “New Onigashima”.
I have a feeling that Caribou might have already tipped Kaido about Shirahoshi.
At the beginning of the arc, Kaidou was hell-bent on killing Big Mom if she set a foot on Wano but when she came in front of him all chained, instead of killing her, he decided to team up with her.
What made him change his attitude towards Big Mom? Yes, he does owe her a favor but that doesn’t justify the teaming-up. Unless he has a bigger plan.
The Marines abolished the Warlord system because they have SSG as their new power. But what do Kaido and Big Mom have to declare war on the World Government? Yes, you are right, the Ancient Weapons.
I am sure that both of them knew before that Ancient Weapons exist. Yet, they decided to team-up now because somehow they have got some insight on the location of the Ancient Weapons. And that somehow was done by Caribou.
Big Mom and Kaido looked so sure about the Ancient Weapons. There is definitely a good chance that they know about the Ancient Weapons’ location which is why they are sure that they can take on the World Government.
*Theory by FireFistRJ