I have looked at all the major airports in the Dominican Republic but there seems to be no direct non-stop flights from the Dominican Republic to Jamaica. I am rather surpised because Jamaica is another major vacation destination in the carribean.
Caribair used to do it but due to some minor issues I believe are without a licence currently....
Jetairfly do Brussels-punta cana-jamaica and back but I'd check to see if you can do the little trip, from what I remember you can't do it. It AA through Miami and a pain at that.
My wife last month took the JetAirFly flight from POP to Jamaica to Brussels flight. Return trip 30 days later however was direct from Brussels to POP.
Check with JetAirFly but unlikely you can do the DR to Jamaica only part.