To use a skin that you have unlocked, go to the main menu of the game and visit the Showcase section. From here you can view your skins and enable one to be used for Batman, the Batmobile, or other characters you encounter during the game. After highlighting the skin, make sure to choose "Select Skin" via the button indicated at the bottom of the screen. This will set it as your Active skin to use in-game.

Skins

Batmobiles