One may not eat anything after eating the afikoman so that he does not lose the taste of the matzah from his mouth. Does this also forbid one to brush his teeth, since that would remove the flavor from his mouth?
 Shulchan Aruch 478:1; Mishnah Berurah §1.
Brushing teeth on Yom Tov has a number of issues to it, such as making the tooth brush wet before brushing, (sechita- squeezing) and the use of toothpaste, (mimareiach- smearing), therefore your question isn’t really applicable. Even if you would have liquid toothpaste, it would still take the taste of the matzoh out of your mouth, therefoe wit to use it until the morning.