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Whilst no one on here is an expert on visas, I think it is safe to say that you do not need a USA visa waiver for the Dominican Republic, because it's not part of the USA! Only if you intend to visit one of the USA Virgin Islands, St Thomas for example, would you need a visa waiver.
If your flight goes via a US airport then you do. I believe the web site to use for applying online without charge is https://esta.cbp.dhs.gov Beware of web sites that impose a charge for the new ESTA application. For more information go to the blue Find a Question box in the Cruise Answers section of this site and within the pulldown list of Topics select Visas. Hope this helps.
If your unsure why not fill in the ESTA regardless. It's free if you use the site given by Bradley & it's valid for 2 years whether you use it or not.