The cry of Morgoth in that hour was the greatest and most dreadful that was ever heard in the northern world; the mountains shook, and the earth trembled, and rocks were riven asunder. Deep in the forgotten places that cry was heard. Far beneath the ruined halls of Angband, in vaults to which the Valar in the haste of their assault had not descended, Balrogs lurked still, awaiting ever the return of their Lord; and now swiftly they arose, and passing over Hithlum they came to Lammoth as a tempest of fire. With their whips of flame they smote asunder the webs of Ungoliant, and she quailed, and turned to flight, belching black vapours to cover her.
It doesn't actually say anything about how fast they got there. "In that hour" simply means "at that time" here. On the other hand, they travelled "as a tempest of fire", which certainly implies magic and speed. Either way, with such inherently magical creatures as the Balrogs, saying that they cannot travel very quickly without flying seems somewhat naive.
Good meme though, always appreciate something that makes me go back to the scriptures.
Perhaps the Balrog underestimated Gandalf, thinking it could cast him into the abyss, then fly back up to deal with the rest of the Fellowship. Alternatively, maybe it calculated that its best chance of defeating the wizard was to grapple with him at close quarters. Either way, the Balrog falling doesn't necessarily mean that it wasn't capable of flight.
Aren’t Balrogs just corrupted Maiar? I’ve never understood why it’s assumed that they all have to be the same. Presumably, they could have taken different forms, either by their own choice, by Morgoth’s, or just by the way the corruption took hold. Maybe some had wings and some didn’t?
Honestly it's not a problem that the Balrog fell. Something that large falling would struggle to stop itself from such a free fall, especially with Gandalf beating it's ass all the way down