"'We can do all our Christmas shopping there!' said Hermione. 'Mum and Dad would really love those Toothflossing Stringmints from Honeydukes!'" (Prisoner of Azkaban 190).
Unfortunately, toothflossing stringmints really do appear only in the brilliant imagination of Ms. Rowling. There is a recipe to be found on a couple different websites (they're all the same recipe, and I'm not sure which site owns the original), but licorice is a major component. It seems to me that licorice is infinitely too thick to ever floss one's teeth. And stringmints are later described as "splintery," which in my opinion negates all possibility of licorice and/or whipped egg whites being ingredients.
So alas and alack, toothflossing stringmints are only to be found in the Wizarding World. If you find a way to make them, let me know! But until then, I guess we're all stuck with regular old dental floss.