The biggest problem here is you're assuming that it's the person who posted another answer that downvoted you. You don't know that. Unless you're sitting there stalking their profile watching all their reputation changes, there's absolutely no possible way to know a person downvoted you. Assuming that will only cause problems for you, as it causes false accusations. It's perfectly possible someone thought your answer was wrong.
Tactical downvoting may exist, but there are just as many people out there who will upvote your answer even if it's competing with theirs. There's even a badge for doing so.
Another thing to consider: don't delete your post just because you got one downvote, especially if you still have a zero or positive score. You get 10 reputation for an upvote, and only lose 2 for a downvote - so you're still sitting at a net gain of 8 reputation. If there are legitimate reasons for your post being wrong or unuseful, someone will comment on your answer. At that point, you can either edit it to make it correct or delete it to remove inaccurate content. If it's correct and useful, others will upvote the answer and that downvote will be meaningless. Don't let a single downvote intimidate you.
As for flagging, you should never do this. A moderator cannot do anything at all to reverse downvotes, and technically the behavior is allowed, so long as they're not mass downvoting (or upvoting) all of your posts at once.