No, Gastly cannot learn to fly.
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No Gastly cannot learn fly in Pokémon HeartGold.
catch a Pokemon that can learn fly, put it in your party, and WALA! you can teach it fly!
Teach it to a Pokemon, enter the Pokemon screen, chose the Pokemon that knows fly and select where you want to fly to.
Go to lavendar town and then enter Pokemon tower in there you can find a gastly.
Gastly is found in Bellsprout Tower.