The new Vivre Cards mentioned that King was with Kaido that time he tried to go to Marineford. I was surprised to read this because I thought it was kind of obvious that he would bring a few people, at least to navigate the ship and stuff. Then I got it.
The Vivre Card mentions it because Kaido only brought King, or maybe King decided to come along. They didn’t need a crew because they didn’t sail to Marineford.
I think that, because of how isolated Wano is, Kaido got the news about the upcoming war just a couple of days too late and there was no time to prepare a ship, gather some troops and get going. But he had to be there because it was his last chance to fight Whitebeard to the death, and then have a go at the Admirals, Sengoku and the entire Marine HQ. So he figured he would fly to Marineford in his dragon form. King, his only Commander capable of flight, tagged along leaving Queen in charge of Onigashima.
It’s also mentioned in the Vivre Card that Kaido hasn’t fought a worthy opponent since Oden and we know that Shanks became an Emperor 7 years ago.
They probably never fought since he got the title, maybe even longer than that. So they clashed briefly, Kaido realized he had met his match and he was at a huge disadvantage because of the terrain (falling down once meant falling in the sea, landing on the Red Force with the entire Red Hair Crew in game mode was straight up suicidal so no hybrid form, trying to sink the ship from above went nowhere). Shanks, who I’m assuming knows about most of the secrets of the world, told him that he would go no further today, but revealed him something about the Void Century that implied the fight would come to him in Wano in a couple of years.
Kaido figured that he would miss it if he died that day and promised Shanks he would come for his ass if it didn’t happen (to which Shanks probably replied “come and get it”). From there on Kaido considers Shanks one of the 5 people capable of defeating him.
This explains why Shanks and his crew got to Marineford looking like a million bucks and faster than expected. The Marines expected a huge naval battle that would wear both sides down and go on for a while, instead it was just a quick intense clash. Kaido went back to Onigashima with some new Void Century information and the promise of the battle of his life two years later.
*Theory by Palmirez