I always take a step back when I see 'implies'... and I"m not sure 'came in a whirlwind of fire' is the same as 'flying'. All the balrogs we hear of are firmly planted on the ground, using darkess and fear as their primary
weapon...including the 'spreading of shadow 'looking like wings' until it stretched wall to wall' in the case of one. (It's true, he also breathed fire and his mane was fire, so he could be said to have 'come in a whirlwind of fire'... but all around him was darkness, much more so than the fire, a careful reading of the passage shows.)
Sauron certainly never flew.
Gandalf never flew.
Saruman never flew. Not sure I can see the 'lesser maiar' as having flown, either.
I can't overcome the clear language of
Tolkien, including his 'figurative language', by potential inferences and implications.
I'll need to search out the passages you have in view sir
@ZehnWaters and see what the language says to me.
Can you provide locations of one or two for me, or close enough to what they say I can find them in a 'search' ?
Thanks.