Easiest would probably going to a US med school, completing resdiency in the US and gaining full licensure here first. Then go to Jamaica and fulfill thier requirements for doctors not educated in Jamaica.
I spent a few minutes looking for specific information from the Jamaican gov't but couldn't find anything. I suggest contacting them directly to inquire how an MD from the US can practice medicine in Jamaica: Jamaica Information Service
Tipton Carlson
Director of Marketing and Recruitment - North America
carlson.t[at]unic.ac.cy
877-298-8189