When
Gandalf says he wields the
flame of Anor I think he is refering of his
sword Glamdring. We know from his battle on The
Bridge of Khazad-dum that Glamdring glitters white. " From out of the shadow a red sword leaped flaming. Glamdring glittered white in answer."(Fellowship of
the Ring pg.429). This glittering could be considered a flame.
Flame-1 : the glowing gaseous part of a fire
2 a : a state of blazing combustion *the car burst into flame* b : a condition or appearance suggesting a flame or burning: as (1) : burning zeal or passion (2) : a strong reddish orange color
3 : BRILLIANCE, BRIGHTNESS
4 : SWEETHEART
It definetly has brilliance and it could suggest a flame or burning. Also, we do not know where Glamdring was made. It could have been made in
Minas Anor which would make one of its
titles "Flame of Anor"
Also, Gandalf telling the
Balrog that he wields this flame is a challenge meaning he will use it against the Balrog. And since he uses Glamdring it is probably the flame.