If Kitesail Freebooter leaves the battlefield before its enters-the-battlefield ability resolves, the opponent will reveal his or her hand, but no card will be exiled.

The exiled card returns to its owner's hand immediately after Kitesail Freebooter leaves the battlefield. Nothing happens between the two events, including state-based actions.

In a multiplayer game, if Kitesail Freebooter's owner leaves the game, the exiled card will return to its owner's hand. Because the one-shot effect that returns the card isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.