If you're on a Legendary Pokémon kick, and you just can't stop, here is another tip on how to acquire one of the three, original Legendary Bird Pokémon. That's right only one, since you won't be able to capture all three.
After you defeat the Elite Four, Legendary Pokémon will start to roam the land, much like in previous games. However, whenever you come across one, they'll immediately flee, not allowing you to do anything from selecting a move or throwing a Pokéball. After more than a dozen times of them running away from you, they'll eventually settle down at the Sea Spirit's Den where you can battle and capture them.
The Legendary Bird you get depends on the starter Pokémon you chose. Articuno will appear if you chose Chespin, Zapdos if you chose Fennekin and Moltres if you chose Froakie.
As always, stock up on Ultra Balls and healing items, and have at least one Pokémon in your party with the ability False Swipe, which will never fully knock out a Pokémon, and instead leave them with only 1HP.