Blackbeard has Gekko Moria on his side, and he can take people's Shadow along with their DF abilities.I think Burgees would give Mingo to Black Beard as he do not have the power to take Devil Fruits abilities, or I'm a missing something.
Actually we have no idea how Blackbeard took Whitebeard's power. Some people assume it's was because of his Yami Yami fruit but the truth is we don't know so Oda can do whatever he wants. But at the least it seems like Blackbeard himself isn't the only one who can get another's DF because of what Jinbei said.I think Burgees would give Mingo to Black Beard as he do not have the power to take Devil Fruits abilities, or I'm a missing something.