CoC is symbolic and it portrays the conqueror, usually those gifted by fate. Only one of millions are born with this ability.
Now you have Luffy and Blackbeard who literally created this new era and both are central figures of whatever will happen at the final war. Blackbeard most likely also knows about the true intention of the WG. He's basically a second Xebec - the one who wanted to be king of the world.
Erkan already gave good evidence to Blackbeard AT LEAST having CoC but again, even Chinjao - another conqueror and CoC user - talked about the difference between "mere conquerors", one of many, and those who can truly shape the world. That's why he was following Blackbeard.
Again, you people just have to follow the story and have to understand the symbolism and meaning behind the core characters. You don't need to see CoC feats of BB to know whether he has it or not. The better question would be: Which CoC version will Blackbeard have? That is something y'all should ask. Not that "BlACkBeArD d0eSnT hAvE CoC!" nonsense...