If you are of the opinion that a vote to close or a review or another action on one of your posts was inappropriate you can signal this to the moderators via a flag, chose "in need of moderator intervention" and explain the issue.
Moderators then can review the situation and, if appropriate, take some action. The action could be, e.g.: talk to the user (moderators have several ways to contact users); in case of severe and repeated problems, ban the user from reviewing; or in excessive cases, even suspend the user altogether. We might also not do anything instantly in a minor case but it can still serve as valuable information. Of course, we might also disagree that there is a problem, in which case we would try to explain to you why we do not see a problem or at least not a major one.
To try to contact the user yourself in such a situation is usual not a good idea, except if you know already and have a good rapport, in which case you likely would not ask the question. I would rather strongly advise not to contact users about such things using channels outside the SE network, even when they do link to their webpage or something like this.
The point is the conversation starts in a negative context. It is quite unlikely something constructive can develop. That said, for general reference, a way to get in touch with users can be chat. Various active users also use chat and you could try to find them in one of the chat rooms associated to the site. It is also possible to send "invites" in chat. I would use those sparingly though.
After these general remarks let me briefly comment on the specific case. At first I did not quite get your description, but I think I figured it out, let me rephrase in a more verbose way what happened:
- User reviews your question (in the reopen queue).
- User votes to "leave closed" your question in the queue.
- User is informed this is an audit, which they failed.
- User goes to your post and votes to close (and possibly votes down).
Now, one may or may not agree with the idea that the question should be closed, but to conclude that the user voted out of annoyance is at least uncharitable. Visibly they were of the opinion before that the question should stay, that is should be, closed. All they did is follow through with their initial evaluation of the question. One might ask if this is an appropriate thing to do. Opinions on this might be mixed, but it is somewhat common that users try to kick a post from the list of review audits, via taking an action on them, if they find the audit is wrong or ambiguous. For the post in question, I personally would likely not close it, but I would also not consider it as a good audit post, since it is does not include much context. It is thus relatively close to questions that should be closed as unclear, for lack of context, and thus it is somewhat ambiguous for an audit post.