Idk what that's from but honestly I don't think it's accurate, Based on the flashback from King in 1036 and Kaidou's own flashback it doesn't seem like King had any fear for Kaidou at all (In the sense that he had true loyalty similar to Zoro and Luffy).
However if we assume it's true: Big Mom & Kaidou could sense Zoro's power when he was unleashing Enma to a restricted extent, this level of power made Kaidou believe he should dodge Zoro's attacks & was shown to cut deeply into his scales.King sensed how strong Zoro was with Enma being unleashed unrestricted and still didn't show fear and was even confident in defeating him, he also didn't show any sign of fear after Zoro revealed Haoshoku infusion on top of that; The only time he showed anything close to fear was when Zoro used the Dragon Damnation attack.
So, if King had any fear of Kaidou it would have to at least be towards Kaidou's Hybrid Form + Haoshoku Infusion or even higher.
In your opinion, which is the weakest form of Kaido that King would fear?