According to the item description:
When you use an action to throw a handful of the dust into the air, you and each creature that needs to breathe within 30 feet of you must succeed on a DC 15 Constitution saving throw or become unable to breathe while sneezing uncontrollably.
If a character (who needs to breathe) snorts the dust, they're not throwing it into the air, so the rules do not specify what happens in this case. See What happens if a character snorts Dust of Disappearance?
As DM, I know how I would rule this (the character would have to make a save), but I am interested in the RAW interpretation. If I'm playing in an organized play context, can I tell my DM that no, according to the book, my character that snorted this dust won't suffer anything worse than if they'd snorted mundane dust (not that I'd ever waste a magic item in such a dumb way)?