Having played MM8 many, many times, I can state unequivocably that yes, having a dragon in the party enables the entire party to fly. I tried the alternative (i. e. killing off the dragons,) but felt too sorry for them to like that side of the quest!
The first time we visited China, Papa Elf and I visited a jade workshop. (By Chinese definition, just about all workable semi-precious stone is "jade." For example, we saw the traditional green jade, and rose quartz as "pink jade.") Papa Elf admired a small "brown jade" (jasper) figurine of a dragon. He is now sitting on our mantelpiece, and his name is "Ithilgore."