The Flute is composed of three separate parts. The three parts of the flute are a cone, a disk, and a cylinder. When the cone and disk are fitted together, they say "The road to truth is the song of dragons". This was inscribed by Matthias Louvier (you can tell, as it is more recent than the other inscriptions on the Flute) and is a quote from a Turkish epic poem, according to Nancy.
The player collects the first part of the Flute after they onto the larger humpback whale in Gatama Atoll to retrieve it for Oceana. The second one is at the bottom of Deep Hole after calming a tiger shark down. The third and last piece is in the HD-9, along with a letter from Matthias.
The Dragon Flute is used as a sort of key to trigger several mechanisms in the Cavern of the Gods, suggesting that the tone or specificity of the vibrations activates a (very advanced) mechanism that then causes an event, like a door unlocking or object moving, to occur.
The Flute sounds a bit like an ocarina when played. It is played by waving it through the water, causing the water to rush through it and produce sound, much like ordinary woodwind instruments are played by forcing air through them.
[Information retrieved with the help of user Jiejies.]