Even barrier ryuo can "hurt" Kaido, whether the scar did anythign more than superficial aesthetic damage is highly debatable, seems like Oda doesn't even bother drawing the new scar half the time and Kaido seemed to instantly recover as he does with everything.
Basic Coc used to clash i.e. against Doffy, Kat and Chinjao.
Luffy is the CoC specialist and general haki master, not Zoro, Kaido was shocked beyond belief that Luffy had it, he would not be shocked if Luffy's 30 broken bone subordinate JUST used it.