[Neithan]

Here are my thoughts on that article.

However, when I have asked people in many forums to try, no one has succeeded. You must use all four parts of the sentence. You cannot drop any part. It is simply not possible to rewrite the sentence so as to show something other than flight. Hence, there is no ambiguity in the passage concerning the Balrogs' mode of travel.

In the final analysis, one must accept that the Balrog of Moria had wings because J.R.R. Tolkien said it had wings, and that the Balrogs flew to Lammoth because the sentence cannot mean anything else.

We shall see about that.

swiftly they arose, and they passed with winged speed over Hithlum, they came to Lammoth as a tempest of fire.

Four parts of the sentence you say? Very well.
1)swiftly they arose--As he points out himself they were underground but even if that were not so it does not follow that they flew. Arose can be interpreted as they were in a sleep or simply idle and when they heard their master's cry they came forth once more. Indeed this is normally how I interpret the word when used in such a context.
2)they passed with winged speed--"winged speed" is an ambigous term. "Winged" is used here as an adjective to describe the word speed not the manner of their travel. Here Tolkien compares the speed of the Balrogs to the speed of flight. As a general rule one does not compare a thing to itself. So here "winged speed" means that they traveled with the speed of a winged creature. Actually when interpreted this way it becomes an argument against Balrogs flying.
3)passed....over Hithlum--this one needs no rewriting, one can run over land just as one can fly over it. Also there is the example of Fingolfin and his horse.
4)Tempest of fire--I see no reason that "tempest" should denote something coming from the sky. As I see it "tempest" could mean either sky or land it rather refers to the fire of the Balrogs erupting in their rath an covering the "battle field" of Lammoth.
So the new sentence would be: "Swiftly they came forth once again, and they passed with the speed of one in flight over(as I said I don't think that this need be changed at all) Hithlum, they came to Lammoth with there flames wreathed about them in a great tempest."
There you have it.

The short answer is that they were Maiar and that Maiar can whatever they please.

The obvious problem is that they had become trapped in there forms and so could no longer fly (assuming they couldn't fly before they became trapped in that form).

"what it was could not be seen: it was LIKE a great shadow, in the middle of which was a dark form, of man-shape maybe yet greater".

This is not the same as saying that the shadow spread out LIKE wings. In this quote he has to say like because to leave it out would be to say "it was a great shadow". But the Balrog was not a "great shadow" it was a being with a physical form that was wraped in shadow. The meaning of "like" changes completely from the one sentence to the other as anyone can see.

I could go on but I am already late for something so I will leave it at that for now.