Here's dictionary.com's pronunciation of
ocarina. As you can see, their pronunciation is "ok-uh-ree-nuh."
To be fair, word pronunciation can change depending on the language. Try typing "ocarina" into this
Japanese-English dictionary (I don't think I can link to the individual word like dictionary.com). The katakana used is オカリナ(o-ka-ri-na). In Japanese, the "o" is a long "o" sound and the "a" is a short "a" sound. So its pronunciation is "oh-kah-ree-nah." If you do look the word up, there is a audio link next to it as well.
I pronounce it with the English pronunciation, though, since as Axel the Beast says, it is an actual instrument.
(Random side note: Wikipedia tells me that "The word ocarina, in the Bolognese dialect of the Emiliano-Romagnolo language, means 'little goose'." How cute!)