Of course you can get the flu! Flu from around the world! This is a tourist destination in the winter.
But there's more than flu — all of it is the "turista". Passage from PASAGES SOUTH:
"In the DR they have an expression for gastrointestinal disorder: la turista. They call it that not because tourists get it, but because tourists bring it. Every winter season they step off their planes shedding billions of microbes and viruses from the common colds and epidemic flus of the northern cities. The little beasties ramp down onto the tarmac and gambol in the tropic heat. Then the whole island acts as a petri dish for the world’s flu cultures.
Dominicans, a touchy folk fond of embraces, kissing and handshakes, provide the germs a perfect medium with which to spread. Thus the winter plague: la turista. How can you avoid la turista between the tropics? Easy. Do what your mother told you to do, and your Psychology 101 professor made you feel guilty about. Wash your hands and scrub under you nails at every opportunity. Don’t poke fingers into any body orifice, including eyes, after shaking hands or handling money until you’ve washed.
And always eat any meat well done. Whatever you do, don’t avoid kissing and hugging."