I wouldn't count on being able to buy flies locally in the Caribean but you might get lucky.
For general prospecting in those parts I would go armed with a selection of crazy charlies, gotchas and small clousers. Add a few deceiver style flies and some wire for toothy critters and your well on your way.
Any of our forum members know the area?
When sight fishing, look over your shoulder from time to time, you never know who's behind you