...I think it's a phoenix.
The colors, Duke! They used black for the ash and red and yellow for the flames.
Maybe they were planning on the fall of Guardia all along? Guardia isn't in 1999 or 2300. Evidence already suggests that the humans constantly have a desire to control life, Crono (kind of) being reborn like a phoenix, becoming immortal was Zeal's goal. You could maybe retcon it to represent the frozen flame? The flying fire that rises from the ashes...of any civilization it touches!
That's a stretch, I know, but why would they choose a crest like that? There are no phoenixes (phoenices?) in trigger, true. There are also no dragons, but there ARE monsters. They chose not to use any mystics but instead a creaure that is mythological even in the Chrono world (until CC of course). With Zeal's crest symbolizing the Mammon Machine, or vice versa, a great emphasis is placed on the meaning of the crest, even from the first time you see a sealed door in the future. Perhaps that was just Kato making his part intense, but I think it means the Guardia crest is as important to the themes of the game. So, yeah. Phoenix.
Any thoughts?