The Pokeflute is a key item in the game, and you obtain it by:
1. Completing the "Get the Flute" side quest in Ecruteak City: Talk to the elder in the Burned Tower, who will ask you to find his lost flute. You'll then need to find it in the tower, and return it to the elder.
2. Using the flute to wake up Snorlax: This is the primary use of the Pokeflute. It is located on Route 12, blocking your path. Use the Pokeflute to wake him up, and you can catch him or let him sleep.
There is no specific "Pokeflute Station" in the game. Perhaps you're thinking of something else?
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