Since it was mentioned earlier that Tira Miron's sacrifice was what made mortals aware of the Silver Flame, and able to communicate with it, I like the idea of the "Death of the Flame" meaning the loss of this comminication.
The Flame in its purest form could still exist, binding the greatest of the Fiends, but the particular physical Flame in Flamekeep could be extinguished, and at the same time, the particular link with humanity could be cut off.
Belief in Eberron is enough to bring spells, but not just any old concept seems to work for this purpose. So, for the sake of this scenario, let us say that all divine magic flowing to worshippers of the Flame is cut off.
Since divine casters are actually the minority of the clergy, a loss of power might not necessarily cause the Church to collapse, but the most proactive good religion on Khorvaire would have lost the power at its heart.
This could lead to a series of fantastic campaign arcs. Do the divine casters among the clergy seek out other faiths, as Tira had been a paladin of Balinor (yes?) originally. Would others, such as the PCs seek to re-establish this contact?
I seem to recall one of the ancient nations that used to be in Sarlona used to have a similar religion long before Thrane. Could clues be found across the sea in the lands of the Inspired? Visiting ancient Couatl lairs, or searching for one of the few who remain. Would the Shulusskar (sp?), bastard children of the Couatl still retain their contact with the Flame? Could they offer hope for the human followers?
If such a campaign did release the Rajah under Flamekeep, I would likely run that as the last consequence of Flamekeep's symbol disappearing, rather than the first. Re-binding such a fiend would prove to be an excellent final confrontation in a world-spanning campaign arc, and lend an additional sense of urgency to the quest.
Edit: Ah, so often I'm the cursed thread-killer
