Since Kaido has been introduced, he has been on a mission to kill himself. By suicide, by meeting someone strong enough to actually take his life, or by creating a war so large it consumes the entire world and maybe being presented an opportunity to die in battle.
Throughout the story, I have thought of many reasons it could be. Maybe he's nuts. Maybe he's bored because there are no challenges for him in this era now that Whitebeard and Roger are both dead. Maybe he wants to be remembered throughout history as well...
During the flashback, Kaido and Oden fought. And, in the end, Kaido won. However, before Kaido claimed "victory", it appeared that Oden was getting the better of him which was a surprise to Kaido himself. The enemy had a transformation technique that showed Oden what appeared to be Momonoske having his life threatened unless Oden surrendered. Oden surrendered and Kaido clocked him over the head.
Knowing what we now know about Kaido's, and from how he speaks, he's an old pirate from an old generation that believed there was honor among pirates. And, while there are no rules in a fight among pirates, his honor was besmirched when taking the victory the way he did. Just one arc before, we saw Katakuri's response when his little Flampe dared to interfere in his fight with Luffy. Injuring Luffy just enough to allow Katakrui to strike what could have been a lethal blow. Immediately upon becoming aware of the interference, Katakuri decided to inflict the same wound upon himself to once again level the playing field and more importantly, to keep his own personal code of honor intact.
Back to Kaido... In the end, he admired Oden. So much so, that he did him the favor of ending his life without further torment. But, once Oden was gone, Kaido's fate was sealed to live with his shameful victory forever.
Oden missing plays a HUGE role in why he is perceived to be invincible... Kaido sincerely believes that there is no other Samurai in the world that will even be as powerful as Oden. This belief is so strong, that no one since has been able to cut him. No one has been able to penetrate his scales. Until now. Now that Oden's scabbards are standing in front him, constantly reminding him of Oden, his belief system was temporarily cracked. They have showed bravery, skill, intense passion and ryou all of which remind him so much of Oden that his shaky belief system was allowing their swords to penetrate his skin. They even strike the very same pose of the attack that once led to his near defeat.
Finally, it is all over. Finally, through Oden's retainers, I am about to die. I am "happy" to die... BUT, after their combined attack failed to penetrate deeper than the old scar left by Oden, Kaido's will/belief that there'd never be another samurai as powerful as the monster Oden was back in full force. With that, Kaido is back to being invincible and impenetrable...
Sorry for the rushed convo... short on time. Please let me know if you agree or disagree.