NO, it is not finished.
The anime finished before the manga:
Anime finished: June 30, 2013
Manga finished: May 09, 2014
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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Aku no Hana follows Takao Kasuga, a bookish high schooler who idolizes the poet Charles Baudelaire and his work "The Flowers of Evil."
After impulsively stealing gym clothes belonging to Nanako Saeki, the girl he admires, Takao is caught by the enigmatic and ostracized Sawa Nakamura.
Sawa uses this knowledge to blackmail Takao, forcing him to participate in increasingly unsettling and disturbing acts.
The anime explores Takao's struggle to escape Sawa's control, confront his own actions, and ultimately, atone for his perceived sins, all while grappling with feelings of shame and the consequences of his initial transgression.