What should I do if I see that a user has posted the exact same problem multiple times? Neither of the questions have answers, so I can't flag the latter one as a duplicate of the first one. Is it okay if I flag it for moderator attention?
Questions from the same user are an exception to the "you can't close as duplicate of a question with no answers" rule. It's precisely for the situation you describe: an Asker has (inadvertently or with intent) posted the same question multiple times.
You should be able to vote to close one as a duplicate of the other even without the target having answers. If you can't (perhaps because the user has created multiple user accounts) then you should flag for Moderator attention.