You can easily check live arrival and departure information regarding flights to and from Dominican Republic airports on dr1.com. The information is listed for Las Americas International Airport (SDQ), Puerto Plata International Airport (POP), Punta Cana International Airport (PUJ), Santiago International Airport (STI), Samana International Airport (AZB) and La Romana International Airport (LRM).
The link is found through the Airline Forum of DR1 where readers consistently post information on airline fare sales and tips for air travel to and from the DR.
See http://www.dr1.com/forums/airline-info/102682-live-departure-arrival-info-all-dominican-airports.html