Does Luffy Have The Strongest Conqueror's Haki. In fact Luffy picked up on how to coat himself in Conquerors Haki by observing Kaidos techniques. To be specific his Conquerors Will.
Only when it clashes with other blackened COA. All his strongest techniques such as Thunder Bagua or Ragnaraku see the usage of this power. The lightning also appears when two conquerors are clashing they dont necessarily have to be using COA like with doflamingo and luffy or when armament and haoshoku combined are imbued into an attack like with kaidos club.
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It has not been confirmed one way or the other but he was one of the strongest characters around at one point and the chijao clash did look like it was CoC based off of the other clashes we have seen involving 2 users. This puts the onus on Mihawk to have it since he is also not a DF user like the other 2 and is a swordsman. He will probably need Conquerors Haki to do that and would be much easier to write if he had it now that we know how it works. The permanent black blades have to do with armament haki and we could see how Zoro didnt know anything about Conquerors haki because Mihawk didnt teach him anything about it since he is not a Conqueror.