So... is Area 88 finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: June 15, 1986
Manga finished: January 01, 1986
... 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
Shin Kazama, a promising pilot, finds himself trapped in a mercenary unit in a war-torn country called Aslan. He was tricked into joining by a supposed friend and must now fight as a fighter pilot at a desolate airbase known as Area 88.
Driven by the desire to escape his contract and return to his peaceful life in Japan, Shin throws himself into combat, becoming a formidable ace. He focuses on earning enough money to buy his freedom.
However, the constant exposure to violence and the harsh realities of war at Area 88 begin to change him. The anime explores whether he can retain his original self and successfully reintegrate into civilian life after experiencing such profound trauma and moral ambiguity.