No, dragon-fire could not be able destroy the Ring. Here's the passage in FotR (chapter 2) that talks about it...
Quote:
It has been said that dragon-fire could melt and consume the Rings of Power, but there is not now any dragon left on earth in which the old fire is hot enough; nor was there ever any dragon, not even Ancalagon the Blad, who could have harmed the One Ring, the Ruling Ring, for that was made by Sauron himself.
Might've been nice if they could've been able do it... but like Nie said, it wouldn't be an easy task.
