Seiryu does get a namedrop in the Stormblood Dragoon quests, so he's a little more real than the Phlegethon Hedgehog. And here's the very minor reference below:
Before I was unceremoniously stuffed into that crate, Ser Alberic told me of the legend of Seiryu─a dragon regarded as a guardian of the Far East.
Though something tells me we would not have much luck with this tale either. The story has existed for several thousand years; Faunehm only came to these lands a mere millennium ago.
They appear to be SOME kind of legend.