I believe Oda has provided us enough information to where we can speculate on the relationship between Orochi and Kaido and how they came to be.
Let’s talk about the article on the Dragons and the importance of them in the One Piece story from One Piece Magazine Volume 5 recently released. This is a hint to us viewers that Kaido is an actual dragon himself.
I believe Kaido is a Dragon and the last of his kind and was once a slave of the Celestial Dragons. He was given a devil fruit for the hell of it (just like the Boa sisters) and the devil fruit, was the Human Human model Oni fruit.
Once he received his fruit and realized he was alone he became lonely and sought a way to die, this caused him to leave Mary Geoise and to seek out the Rocks Pirates. On the Rock Crew he was kept in check by Captain and decided to follow him. Somehow, Someway the Rocks Captain gets defeated by Garp leaving Kaido alone and without his captain.
So he sought death again and this time was captured and was in and out of Marine facilities being experimented on by Vegapunk at Punk Hazard and King his jailer.
King begun to respect Kaido because he was never injured and his will was never broken thus leading him to help Kaido escape.
I believe once they escaped they settled on Onigashima Island, the Island that Kaido said his ancestors resided.
Oden Kozuki went around the country of Wano gaining respect and defeating those territory bosses in the country. I believe Orochi was a territory boss who envied Lord Oden and he only followed him because he was defeated.
When Lord Oden left I believe this is where Orochi saw his chance to defeat and get even with Oden. Orochi with his devil fruit already then went to the deserted Onigashima Island to see if he could find something to use against Oden. There he ran into Kaido but not as a human but as a Dragon.
Once this happened Kaido must have thought Orochi was a dragon just like him. Orochi told Kaido that since they are both dragons they must help each other and this formed the alliance that killed Lord Oden and ruled Wano Country.
*Theory by PutSomeRespeckOnLaw
