The “Man with the burn scar” has the same disease that Law did as a child and that’s why he reacted like that. He knows it’s not really a burn scar but instead from Amber Lead Disease.

Amber Lead Disease ravaged through his hometown and Law would know the symptoms better than ANYONE. Whether he’s seen him is up for debate but I believe the man has or had the same disease Law had as a child yet was able to cure himself with a Devil Fruit similar to how Law used the Op Op fruit to cure himself.

Doflamingo himself believed that one could cure the disease if they possessed the correct Devil Fruit so it may by tied to his ability to summon whirlpools which we still don’t know its full effects besides that.

His disease marking his body in the shape of flames instead of really being burned makes way too much sense to me.

PS: Also I believe the government is forcing him to protect the poneglyph because of his Devil Fruit but this is a long shot even more than the theory itself lol.