you have to go from the dj ben's radio station and go left, then go up between Mary's (or whatever it's called) station and it should be around there.
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In Pokémon HeartGold, you can find the White Flute in Route 47 in the Johto region.
You cannot get the Azure Flute in HeartGold. The Azure Flute is only capable of being used in Pokemon Diamond or Pearl. The Azure Flute can only be obtained by an event of some sort in Diamond and Pearl.
While the Azure Flute does exist in HeartGold and SoulSilver's files, the Azure Flute cannot be traded to these games. There is also no event to capture Arceus in these games, thus trading the Azure Flute would have no point.
You will have to move that circle thing to the very top of the radio, then it will say poke flute at the top.
Yes there is a Global Trade Station in Pokémon HeartGold and SoulSilver. It is located in GoldenRod City in the west.