Not aware of an anime-specific kbin server, but there are anime focused Lemmy instances like ani.social that are accessible through kbin.social and anime communities on both kbin.social and various Lemmy instances. I’ve been posting to [email protected] and [email protected] recently and occasionally in a few other places.

@MentalEdge has a post with a list of communities that may be of interest as well: https://reddthat.com/post/123968

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Bit late to the party, but:

There’s https://kbin.social/m/Anime, though it’s mostly dead aside from the microblog functionality and most seem to have settled on Lemmy at https://lemmy.ml/c/anime and https://lemmy.world/c/anime (.ml being more active than .world)