So... is Chikkun Takkun 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
In the far reaches of space, the powerful "Waruchin Ceremony" is stolen from the planet All Star by the nefarious Doctor Bell.
This ceremony possesses a unique computer capable of manipulating reality, and Doctor Bell plans to use it for galactic conquest.
Determined to stop him, Prince Chikkun of All Star, accompanied by his intelligent advisor Takkun, journeys to Earth to recover the stolen artifact and thwart Doctor Bell's evil schemes.
Their adventure promises a chase across Earth as they try to outsmart the villain and protect the galaxy from his ambition.