For a taste of authentic Caribbean flute playing try Jose Fajardo's recordings; a favorite is: Jose Fajardo's All Stars, "Cuban Jam Session". Fajardo is generally considered the king of Cuban flute playing, with great style and a unique sound due in part to the fact that he played the traditional wooden Cuban flute with only five keys. More contemporary Latin flute players play the Boehm silver flute. Try also the recordings by Nestor Torres and Johnny Pacheco. If you can find them, the early Eddie Palmieri records featuring Johnnny Pacheco are killer.
Most of the suggestions so far, while very good ones, are not really what I would call authentic Caribbean music. Caribbean influenced, but not the real shit, as they say. Even Valentin is more of a crossover artist, playing in more of a Latin Jazz Fusion style.
I imagine myself on a warm sunny beach somewhere in the Caribbean and I think that the music that I would hear is more along the lines of Fajardo or:
-Cachao "Master Sessions". Great Cuban bass player with a variety of Latin stars such as Paquito D'Rivera and Nestor Torres.
-Cubanisimo! starring Jesus Alemany
-Best of Los VanVan
-Buena Vista Social Club
-Anything by Orquesta Aragon, the "charanga" masters.
For me, nothing defines the sound of the Caribbean like the sound of a traditional "charanga" band: rhythm, flute and strings. More subtle than most salsa bands but can swing even more; a great sound.
Enjoy and don't forget the Appleton dark Jamaican rum, over ice.