Actually, it is not entirely clear what happened to the Flame Imperishable at the beginning of the universe. The most direct reference is from Ainulindalë, where Ilúvatar tells the Ainur, 'And I will send forth into the Void the Flame Imperishable, and it shall be at the heart of the World, and the World shall Be; and those of you that will may go down into it.' From the phrasing here it is unclear whether 'the World' means 'the entire universe' or 'the Earth', and other similar passages seem to show the same ambiguity.

Perhaps the most plausible explanation is that this is a creation story in the mythical mould, where the Earth occupies an overwhelmingly central role in the cosmos, so that the two meanings of 'World' are fully intertwined with one another. We see this idea illustrated elsewhere: for example, Varda 'paints' stars onto the sky with the dews of Telperion - a notion that only makes sense in a fully geocentric universe.

If we follow this line of thought, the 'mythical' universe was lost, and the physical came into being, at the time of the Downfall of Númenor, when the West-that-was was taken away from the world, and the world itself was made 'bent' (that is, round). What this profound separation would have meant for the Flame Imperishable, we are not told.