Mostly it's whether I see accounts breaking the site guidelines:
https://news.ycombinator.com/newsguidelines.html. That includes swipes, putdowns, name-calling, ideological/political/nationalistic battle rather than curious conversation, fulmination, cross examination, repeating internet tropes or talking points, and so on.
I don't know what you mean by "openly show how both sides are affected". That's a tricky business. Everyone with strong feelings feels like the mods are biased and few are persuadable otherwise. Most people (with strong feelings) would be satisfied by little less than "promote all the posts I agree with and ban all the commenters I disagree with", though they don't phrase it in those terms, presumably even to themselves. It just works out that way in practice because when strong feelings are involved, all opposing comments tend to feel false and/or trollish and/or abusive.
What I can tell you for sure is that we're moderating all sides of this topic, same as with any divisive topic, when we see the site guidelines being broken, and we do our best to be even-handed about it. That doesn't mean there's no bias (unconscious bias is a thing, and total absence of bias is surely impossible), but it does mean that we work hard and consciously at it, and have many years of practice in doing so.
p.s. when you ask "What makes you flag something as flamewar", I suppose I should clarify that most [flagged] posts have been flagged by users, not moderators. Mods do flag some though.