It is possible. I have never done it but those I asked who have done it say they used a third party shipping company. You sign up with them and use their US address to have the products sent from Amazon. They determine with Customs the duty and give you a final price. You pay and then they fly it to Jamaica and a local courier service (DHL, etc.) will deliver it to your door.
My neighbor tried to order through Amazon and went through the roof when he got the final price. He could order the product from Pricesmart in Kingston and have it delivered for nearly half the price. Pricesmart is affiliated with Costco as they sell Kirkland brand items.
Remember that you will have to pay for the flight and the ground delivery as well as the Customs duty. If you can get it here, it is always the better solution.
