I'm not sure how to flag a user, but https://workplace.stackexchange.com/users/10072/user10072 seems to have been just posting a spam answer in several questions. I know I just confirmed flags for at least 2 of his/her posts. Is there a correct way of bringing users like this to diamond's attention, or is flagging each spam answer the correct way to go?
Flagging each spam answer would probably be sufficient.
You can't directly flag a user, but you can flag any of the user's posts with a custom flag and explain the situation.
Just FYI, spam flags are handled a bit specially on the SE network, and enough spam flags will automatically hide posts by that user and give a heads up to the moderation team to take a look at it. This is usually done very quickly (the same user posted a similar message on academia, and perhaps Super User as well).
If you see spam, flag it, and then if you feel so compelled, hop in to chat and just say "Spam:" and post a link to the question (it will 'onebox' the post in question so we can all click directly to it).
If the post still exists in 15 minutes despite this, you can raise a custom flag for the moderators (as Jim suggests), and/or you can hop in to Meta Chat which usually has users who can handle it if you link to it there. This should rarely be necessary, since most of these sorts of posts are caught and dealt with very very quickly.