As it makes the Pokémon become the center of attention, in addition to its usual effect... So, for it to work it has to gain priority right?
The center of attention means that it will become the target Pokemon, hence it really only becomes useful in doubles.
The only real ways to change the prioitry of this move would be quick claw activating or Prankster.
No Z-Destiny bond will not gain any extra priority.The only factors that will affect the priority are speed, typing and trick room.