So... is Flaglia: Natsuyasumi no Monogatari finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Flaglia: Natsuyasumi no Monogatari tells the story of young Iko and his four older brothers as they spend their summer vacation together in a seaside town.
Iko adores his siblings, who act as his guardians since their mother is away working in Tokyo.
Unbeknownst to Iko, his brothers harbor a magical secret; they are wizards with exceptionally long lifespans.
The anime explores the everyday life and bonds of this unique family, balancing their seemingly normal summer with the hidden world of magic that surrounds them.