Being the only U.S. president who spoke English as a second language, I can only hypothetically assume he had one during his youth. But as he served his way to the point of being elected president did the man pronounce his R's with the distinctive thickness of a Dutch accent?
This has been asked before; http://www.reddit.com/r/AskHistorians/comments/1nt2s3/martin_van_buren_was_the_only_us_president_who/
You're assuming Jersey Dutch was pronounced like modern ABN. It wasn't. http://www.dbnl.org/tekst/_tij003191301_01/_tij003191301_01_0032.php
So even if he had a Dutch accent, it wouldn't be the Dutch accent you're thinking of.