So... is Himitsu no Akko-chan finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: October 26, 1970
Manga finished: August 03, 1965
... 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
Himitsu no Akko-chan follows Atsuko "Akko-chan" Kagami, a spirited young girl who loves mirrors.
When her beloved mirror breaks, she treats it with unusual respect.
As a reward for her kindness, a magical being grants her a special mirror.
This mirror allows Akko-chan to transform into anything she desires using a special enchantment.
The story revolves around Akko-chan's adventures and experiences as she uses her newfound power for various purposes.