Well, not really. Because canonically, a phoenix nearing the end of its life would set itself a blaze, and from its own ashes would rise once again thus symbolising the constant circle of rebirth. So, her dying from the fire is actually pretty accurate. The only thing that is a bit iffy is that she died due to the smoke but if her body was burned by the fire by the end of it, which we can assume it was, I think it's still a pass mythology-wise.
Oh well the author's not wrong abt it
There are lots of mythology stories about the Phoenix but the common thing of all their stories is that the Phoenix dies and was reborn through the fire...though I do think that the author made a mistake or made it on purpose because when a Phoenix dies through the flame they dont regress, they reborn or they resurrected. It would have been more accurate if the timeline changes as she was reborn but I know the author doesnt have that in mind. Oh well, its the author's choice at least the author made some research, yea?
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Phoenix died from fire, wow. Or is it more from suffocation by smoke? Nevertheless, that sounds ridicilous. That's like saying a mermaid died from drowning.