So... is Honoo no Tenkousei finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: May 21, 1991
Manga finished: November 01, 1985
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Noboru Takisawa, a new transfer student, arrives at a school where boxing determines everything.
He soon discovers that conflicts, big or small, are resolved through matches in the ring.
Driven by his feelings for Yukari and a desire to prove himself, Noboru finds himself constantly challenged.
His main rival quickly becomes Ibuki Saburo, the school's dominant force, setting the stage for intense boxing showdowns.
Noboru must navigate the school's unique rules and overcome his opponents to earn respect and win Yukari's attention.