You said Flame was assumed to be the prophecy kit. What’s the situation with that?
Ha, yeah. So Flame and Fire look nearly identical when they're kits. They get more defining features when they age, but they still look like either of them could be the fire in the prophecy.
Not knowing which is which, Bluestar ensures they both have high ranking mentors (she assumes the prophecy is about the future leadership of Thunderclan). Flame is given to Redtail, and Bluestar gives herself Fire. Flame is later given to Goldenflower after Redtail's death.
As the lovely @Bonefall once pointed out, canon Firestar seemed to have gotten a solid amount of his leadership style from Bluestar. Who, in comparison to the other leaders, is much more selfless and righteous... yeah this Bluestar isn't like that. And, as a result, Fire picks up less positive traits from her.
Flame, in comparison, is much kinder. Bluestar high key trains up Fire to eventually become leader as surely he's the one whose got what it takes.
Anyway, when Tigerclaw is discovered, Bluestar is about to make Fireheart deputy. She looks into his eyes and sees...herself. That is what Starclan wants? That is the future of Thunderclan? More of this? Call it a revelation, call it hysteria, but she names Flamesong as the new deputy cause fuck Starclan.
The funny thing is... she was right in her moment on high rock the night of Tigerclaw's betrayal. It's too bad even Starclan isn't as all-seeing as they claim.