So... is Seikoku no Dragonar finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 21, 2014
Manga finished: November 26, 2016
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
Ash Blake, a student at a dragon riding academy, is considered a failure because he can't summon his dragon. Despite having the mark of a dragon master, he's the laughingstock of the school.
His luck changes when his dragon finally appears, but not in the way anyone expected. Instead of a typical dragon, it's a beautiful girl!
This new dragon, with a strong personality, immediately asserts her dominance over Ash, turning their relationship dynamic upside down. Ash's dragon riding problems are far from over; in fact, they're just beginning.