So, I chose Froakie as my starter in Y, so I can find Moltres. I go to Moltres in the pokedex and it says it is in Rt. 19. So I fly to Snowbelle City and go to the right to Rt. 19. Next thing I know it is in Rt.12. So, I fly to Shalour City and head to Rt. 12, and now it's on Rt.22. How can I track this thing down if it keeps moving?
Never fly to the place!What you should do is fly to a random city. Then you check the location of Moltres. If it's in the nearby route from the city, go to the route. If it's far away from the city, fly again to the same city you are in! Then check its location again. Keep doing this until Moltres' location is shown to be on a nearby route. Walk to the route and have a Pokemon around level 70 in the first slot of your party. When you encounter him, he'll run away. Repeat this method all the time until it's location is shown to be in the Sea Spirit's Den. There you can battle him and catch him. But remember to not fly to its place because that resets the place! Hope you catch him ;)
After defeating the Elite Four, several Pokémon start to roam the region, Articuno, Zapdos and Moltres. However, you will only get one: Articuno if you picked Chespin, Zapdos if you picked Fennekin and Moltres if you picked Froakie. However, a change has taken place compared to previous games. These Pokémon will automatically flee from combat, before you even get a chance to select a move. You can track their location with the Pokédex. After they have run from you over a dozen times, they will go to the Sea Spirit's Den where you can finally battle them ~ Serebii
Just keep running into Moltres, and eventually it will appear in Sea Spirit's Den after about a dozen times.