Gandalf's beams of light

[Angry Hill Troll]

The meaning of Gandalf's statement to the Balrog

I am a servant of the Secret Fire, wielder of the flame of Anor.

is discussed
here. I personally don't think that either the light that Gandalf emits or the "flame of Anor" to which he refers is directly related to Narya. I think it is rather a manifestation of his Maia nature, and perhaps some of the light of the Trees. Anor (the Sun) is after all the last fruit of the Golden Tree. In this event, the light which Gandalf gives off in these instances would indeed be related to the light in the Phial of Galadriel, since that light was from the Silmaril borne by Eärendil, which preserved the light of the Trees.

Recall that Tolkien says that the Noldor won the Second Battle against Morgoth in part because "the light of Aman had not yet dimmed in their faces". It seems possible that Gandalf, as a Maia, might be able to preserve the Light indefinitely, to use when needed.