In elementary school, between '92 and '96, I read a young adult fantasy novel that has eluded my internet searches to this day. I don't remember the plot, but I think it had the word 'Rainbow' in the title. There was a dragon that the main character, and adventuring party, was flying on at the end of the book. The bad guys (?) cast a magical web in front of the dragon at the end of the book, and the characters fell. It just stopped there! It was probably part of a series. I can't remember much else. Any help is appreciated.
This is a long shot - but the 1993 novel 'The Iron Dragon's Daughter' by Michael Swanwick has a chase scene near the end of the book, in which
the protagonist, a girl named Jane, and her dragon Melanchthon are being pursued by other 'dragon pilots' (in this world, dragons are magical/mechanical, somewhat malevolent constructs). They do fall, as do their adversaries, after being slowly destroyed by the environment through which they are travelling (a 'super-reality' in which the goddess of their existence resides).
However, Iron Dragon's Daughter does not end at that point, but continues for two chapters of resolution, so, again, it is a long shot. Also, it was not written for young adults, so if you read it in elementary school there could be quite a few bits that didn't quite sink in.
Incidentally, Swanwick wrote a sequel, The Dragons of Babel, in 2008.
Could it be one of the Dragonriders of Pern series by Anne McCaffrey?