I've met Zapdos, but it always flees. That sucks, I dunno what I suppose to do. Maybe I should take Pokemon with Shadow Tag ability with me or something.
In order to get Moltres/Zapdos/Articuno(depending on the starter you picked) you will need to encounter them 11 times. It is normal that they always flee before you can even select a move. After the 11th encounter you will have to go to the Sea Spirit's Den.
here you will be able to battle only one of them at level 70