For starters do not fall for the trap of paying hundreds of dollars to Universal or any of the flight planning companies to get you a cuban overflight permit.

try www.caribbeanflyingadventures.com they will get you all you need

CUBAN OVERFLIGHT PERMITS

Grand Cayman's FBO


Flying over Cuba is easy and interesting - an exciting experience! But IFR only
1) Complete and Submit Request Form - (Click here) at least two working days prior to departure (not counting Sundays)
2) Private Recreational Flights - Click here to purchase permit (free for members)
3) Business and Commercial Flights - Click here to purchase permit
4) Cayman Operating (landing) Permits for part 135 - Click here to purchase permit
The U.S. Treasury Department recently issued a decision prohibiting U.S. citizens from contacting Cuba directly to obtain overflight authority. A number of companies are licensed to obtain permits for you - for a fee ranging from $160 to $2,000.
Private Recreational Flights are not assessed overflight fees; these are defined by the Cubans as owner-operated aircraft flying to the Caymans, Jamaica, etc for family holidays; flights that are flown by owners but for business purposes (one day trips) or Charters or Corporate aircraft are charged "navigation fees" and "transaction fees" that must be paid by wire transfer to a Cuban account in a Panamanian bank. In addition, for flights operating above 24,000 feet, there may be a "navigation" fee assessed by Jamaican flight service IF you are in radio contact with Montego Bay FSS.
Caribbean Flying Adventures is authorized by the U.S. Treasury to work directly with Cuba's Civil Air Authority. We will obtain your one way or roundtrip, Cuban Overflight Permit free of charge for subscribers - one per year. Additional permits or amendments to existing permits are $40. Havana will not process requests received less than 48 hours prior to departure and they require at least one hour's notification prior to your arrival at the boundary (which simply means you should file your IFR flight plan at least 90 minutes prior to departure to be on the safe side.

Kingston is very dangerous--do not plan on leaving your hotel at night.