Each airline is different. They are all constantly changing their rules. i just looked up two United and JetBlue. For a Kite Board less than 100 pounds the cost is $50 each way. Cape Air has their own very lengthy carribean rules on their website. Here is what United has to say on the subject:
The service charge for a surfboard, wakeboard or paddleboard is $150 (each way) for travel between the U.S., Canada, Puerto Rico and the U.S. Virgin Islands, and $200 (each way) for all other travel.
