[Finwe]

I'm afraid that second assertion is impossible. All of the Silmarils have been accounted for, and none of them are in Aman, save one. Earendil bears one upon his brow as he sails in his ship. The other two Silmarils were lost in the fires at the heart of the earth and in the sea, respectively. There is no chance that the jewel on top of Gandalf's staff is a Silmaril.

I think that what he means when he says the "Flame of Anor," is the Flame Imperishable. All of creation is made out of that flame, it stands to reason that the Ainur should be too, at least their physical bodies. It was said that when they walked without a fana (body), they were as a naked, white flame, the Flame Imperishable. Thus, Gandalf, in fighting against the Balrog, would be wielding the Flame Imperishable, and thus, the Flame of Anor.