Same day as all consoles.
Unfortunately the Batman themed skin pack isn't in the in-game store yet.
Mortal Kombat 11 game, Kombat Pack and bundle are all on Pro discount right now.
Edit: The Batman themed skins are in the game, you don't have to buy them like other skins. You do have to manually set them like other cosmetics. The skins are for Noob, Baraka, Kitana and Geras.