Comprised primarily of firebenders, this organization wants to see the Fire Nation restored to its former glory and dominion over the rest of the world.
They have factions all over the world, keeping watch and keeping wrath and holding grudges among the very cities they're assigned to protect. They are in allegiance to the old ways, subjugating the world and ruling with tyranny and fear if it means they're given the respect and awe they think they deserve. They secretly plot the demise of Fire Lord Zuko and his sympathizers... And they're always watching.
Generally speaking, the leaders of this organization are from old money, old power, and know what it tastes like to be in complete control. Noble by blood, not quite so in their intentions. They're all loyal to the Fire Nation above all else, willing to sacrifice just about anything - they were even unopposed to genocide, once - to accomplish their goal of reconquering the other nations with a puppet ruler on the throne.
Unlike it's counterpart the Jade Shark, the Flame is all about careful planning, spies, secrets, quiet assassinations. They hate making a scene, hate bringing attention to themselves, and pride themselves on working right under Zuko's nose most of the time. They're armed with intelligence and war experience, after all. They know how to work the system when they once helped create it.
The majority of the organization are loyalists, ex-soldiers, impoverished firebenders wanting to recapture the fame and fortune of the war days. They work in small groups scattered through the nations; the leaders of these groups are called Alphas and those who fund these alphas are an elderly Senate of six chairs. The Senate is paramount in all things, viewing themselves as a higher power, even, than the Fire Lord or his counsel.
The lot of their funding is earned through RatHound racing in the Earth Kingdom. It's a well known fact that nothing runs faster than an Ember Island RatHound. The rest comes from the noble members themselves, or other loyalists willing to lend a few coins to the cause in return for the promise of prosperity beyond their wildest dreams should their efforts come to fruition.
Initially, the Flame sought to restore the fallen Phoenix King to his usurped throne. They managed to smuggle him out of the Boiling Rock and harbor him in Shu Jing. But as is the way with even the best-laid plans, Ozai got a tad greedy, made some rash decisions, and subsequently put himself in the Senate's bad graces. Their back-up plan, "domesticating" the ex-princess Azula, only promises marginal results. Another meeting of the Senate seems inevitable; it's time for more sinister plots to be hatched.