So... is Ao no Kanata no Four Rhythm finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: March 29, 2016
Manga finished: March 26, 2016
... 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
Ao no Kanata no Four Rhythm tells the story of Asuka Kurashina, a newcomer to an island archipelago where people use special shoes called Grav-Shoes to fly. This technology has led to the creation of a popular sport called Flying Circus.
Asuka unexpectedly discovers her talent for Flying Circus and joins the Kunahama High School club. She learns the ropes alongside Misaki Tobisawa, an experienced player, and Mashiro Arisaka, Misaki's close friend.
Under the guidance of their coach, Masaya Hinata, the club members work together to improve their skills in Flying Circus. The anime focuses on their journey as they pursue their dreams while facing the challenges and uncertainties of the future.