In chapter 1049 we see some pirates reacting to the news of the defeat of the Rocks pirates and one of them says:
“I bet their infighting finished them off. None of them had the team spirit…” The next image shows a young Big Mom looking quite pissed off and saying, “Don’t fuck with me! Where the hell did you go, Kaido?”
The next image is of Grandma Kurozumi saying “10 years have passed since that incident, Kaido… You are now known as the embodiment of brutality”.
The first two imply that for some reason Kaido decided not to help Rocks during the fight anymore. The third implies that something happened at God’s Valley that helped make Kaido “the embodiment of brutality.” The way she says “this incident” instead of just saying what happened could also mean several things.
Big Mom gave Kaido his Devil Fruit when he was on the verge of death. My guess is Kaido got wrecked at God’s Valley, Big Mom gave him his Devil Fruit and once he learned how it worked he turned his back and ran away.
Maybe Kaido was ashamed of having suffered such a defeat. He was ashamed of having abruptly abandoned his former teammates to save himself, a side of him that still seems to come out when he’s drunk. That’s why Big Mom is furious that she can’t find Kaido in this flashback.
An Incredibly Powerful Devil Fruit
With an incredibly strong Devil Fruit on top of his already impressive strength. It’s no surprise that Kaido becomes the epitome of brutality. Looks like Kaido has a lot of resentment towards himself and the world. I think it’s because something happened at God’s Valley that showed him the true face of Rocks.
This could be why Kaido is so determined to break the spirits of young recruits and so sure that Luffy’s alliance will end in betrayal. He wants to believe that, given enough pressure, everyone would have done what he did.