I would vary the above directions only a little bit. I did that drive twice over the past two weeks.
As you come into Santo Domingo, do stay on John f. Kennedy, following the signs to the Aeropuerto/ always take the elevated portions -the two left lanes--until you come to the Olympic Center--You can see the big stadium on your right. Ahead you see a half moon type pedestrian bridge. Go to the far right lane, and as you come to the intersection, turn right. that is M?ximo G?mez. Go to the next major intersection and turn left. That is 27 de Febrero. Now you take one of the far left lanes and off you go to the airport.
(The reason i suggest this is that going under 27 de Febrero and then up onto the elevated portion can be rather confusing. For those of us who do this frequently, i find that using Maximo Gomez is the faster route)
Cordially
HB