Someone laughs off the attempt to start a Flame War, and the person who tried to do it doesn't persist.
The Flame War consists of maybe five posts before the moderators handle it.
The issue that causes the Flame War is actually Serious Business to some degree and people will obviously have very polarized feelings on something where no agreement between the sides can be reached. Good (or bad) examples here are most if not all religious and political and cultural flame wars, because agreement between the sides (as opposed to tolerance of the other's differences but continuing disagreement) would mean one or both sides giving up issues of deep principle or culture to reach a compromise.
A discussion or place online devoted to trolling, insults, intentional Flame War, or the like.
The Flame War is fighting back against Trolls or others such as the Spammer using invasion tactics on a person or discussion venue.
The discussion is "Worst Flames" or "Start A Flame War" or similar.
A discussion or place online where help, useful advice, or some other form of cooperation or useful assistance is far more predominant than fighting.
A discussion or place online where the people are all pacifists with the occasional Technical Pacifist or Martial Pacifist moderation to deal with trolling and not in the sense of arguing over pacifism - in the sense of putting it into action.
A Troll posts some inflammatory message that actually doesn't upset anyone, and no one even responds to it.
Double Subverted: A discussion that would never seem to possibly be anything anyone could become sincerely angry over starts the biggest Flame War in history, ascending to Internet Backdraft status and then to offlineMemetic Mutation. One good example of this happened some years back when a Japanese Youtube user posted video of a thunderstorm. By the time the war was over, everything from religion to the atomic bombings of Hiroshima and Nagasaki had been fought over in the comments...
A moderator sees someone flaming and bans them. Things quiet down, but then people who are friends of the banned user realize what happened, and begin to flame the moderator in the thread, reigniting the Flame War, but over the ban rather than the original topic.
Internet Backdraft, Holy Wars in general, and meta-flamewars are always Zig Zagged Flame War, because the actions taken to stop the flamewar become part of it, as do the people demanding it stop, as do the people continuing it or continuing drama related to it.
Flame War just doesn't happen.
Moderators and admins put in very strict rules to prevent Flame War from beginning and starting or getting involved in one is an instant ban offense.
A certain Image Board, and some other places where the intent is to be as offensive and assholish as possible.
"Atheism vs. Christianity, which one's better guys?" posted almost anywhere.
"What does your religion say about sex?" posted almost anywhere.
"So I'm having problems running Game X on my Mac..." posted to anywhere that isn't a Mac-specific community
The posting of a hit piece or outright Demonization of a community or group anywhere many members of that community or group frequent.
Starting drama and Flame War for attention or to make one look more like an expert than one is.
Starting a Flame War to distract people from something more important.
Reverse trolling: after an incident of abusive behavior, for example, where all the activity was via private message or deleted before anyone could act, a mod or an ally of the attacked people flame baiting the trolls/flamers into an attack on them - and then banning them and/or screencapping the proof of how pointlessly abusive they are.
People ignore the Troll or respond intelligently and calmly to the inflammatory post.
The combatants decide it's not worth it to have another flamewar over the same subject with the same people and walk away.
A discussion venue dedicated to politics, religion, sex, or shipping debate has no flamewars or no real flamewars.
Moderators, admins, or owners discuss what topics will not be allowed for discussion to prevent inevitable Flame War.
"This is beginning to look like a Flame War, people really need to calm down."
Conversed: Fandom Wank or similar communities that exist to comment on Flame War and those involved in it.
"Whatever you do on that board, do NOT bring up whether Alice should be with Bob or Carol."
A thread exists - but with a ton of deleted or removed posts and/or a lot of banned users.
Plotted A Good Waste:
In-Universe, a Flame War is depicted to show the pettiness or stupidity of those involved.
In-Universe, a character has to deal with Flame War repeatedly, and this establishes why that character has such a misanthropic view of the internet/of humanity in general.
Deconstructed: There's NO way to "win" a Flame War. Sane people eventually realize how silly they are being and stop... Leaving only a bunch of stubborn jerks to fight over the ashes of a dead horse.
While there is no way to "win" a Flame War, the subject was of some importance and some of the posts did serve to convince some of the less strident individuals to open their minds.
In a similar way, the point of the Flame War or the angry response to the Troll} isn't out of seriously trying to convince that person of their own error, it is to demonstrate to anyone looking on that their conduct is unwelcome. If someone is saying insanely bigoted things or singling out individuals for personal abuse, for example, flaming them may be seen as a way of discouraging such behavior.
Similar to both of the above and the justified example with the Spammer, it is known that one side of the "debate" is operators of the Sock Puppet or an Astro Turf attempt. The Flame War in this case isn't intended to actively convince the sockpuppeteers or astroturfers - which is likely impossible - but to combat the sockpuppeting or astroturfing itself and to make those doing it go away.
Played For Laughs: A silly intentional Flame War where everyone is in on the joke and no actual offense is intended.
Played For Drama:
The Flame War invokes Real Life consequences in some way.
People chase down those involved in the Flame War elsewhere online to harass them, becoming Trolls, the Garbage Post Kid, or stalkers because some debate on some forum somewhere has become very personal to them.
U think that? Ur st00pid and ur mama did it with a dog. Gb2 Flame War!