Hi Ricky.
Lodge Mt. Olive #336 under the GL of Scotland. So far as I'm aware, this is the only Lodge (of any jurisdiction) which meets in St. Kitts.
It meets at 8 p.m. on the 3rd Thursday of each month from October to June, at the Masonic Hall, Taylor's Range, Basseterre, St. Kitts.
Be there an hour early, because Scottish proving tends to be thorough. Take your GL certificate/diploma as well as your dues card, because the British GLs like to see the certificate when they're proving you - in British practice, this is even more important than showing your dues card. Get an introductory letter from the GSec of GLoTX if possible. Take your own regalia, because in British practice it is usual for each Brother to have his own - British-jurisdiction Lodges don't necessarily carry a stock of borrowable regalia. Wear a dark suit, white shirt and tie, because British GLs demand a conservative dress code - in the Caribbean you might get away with a little less formality, but don't rely on that being so.
Bear in mind the protocol that visiting outside one's own jurisdiction should be arranged through the respective GSecs. You should ask your GSec to contact the GSec of the GL of Scotland, and he should get back to you with contact details for the Lodge Secretary, whom you should call when you get to the island.
Enjoy!
T & F,
Huw