Is there any link between being a D and emperor's haki?
Conqueror's Haki is very rare ability that only 1 in a million can get. Unlike Armament and Observation which can be gained through training, Conqueror's Haki cannot. You must be born with it.
Those with Conqueror's Haki are said to have a qualities of a King (or Queen if female). Which the show has shown with Roger (Pirate King), The YONKOs (Emperors), Hancock (Empress), and Doflamingo (Celestial Dragon).