Gelukkig Nieuwjaar
This is a direct translation of "Happy New Year" and is the most widely understood phrase.
You can also use:
* Proficiat met het nieuwe jaar: This translates to "Congratulations on the new year" and is a more formal way to wish someone a happy new year.
* Een gelukkig nieuwjaar: This translates to "A happy new year" and is a more literary way to wish someone a happy new year.
Keep in mind that Flemish is a dialect of Dutch, so "Gelukkig Nieuwjaar" is also understood in the Netherlands.