The most popular theories I've heard about Set have been that His animal form either is a) a mythological "Typhonian" beast that is unique to Him, or b) some ancient desert hunting-dog that is now extinct or highly endangered.
In fact, a few years ago I believe there was a wild desert dog that was killed and brought in, who had the forked tail, square ears, and other parts that Set has. The locals call it a "Salawa", but I'm not sure if other specimens have been found. In any case, chances are Set is not really a "kitsune" per se, although I'm sure there could be many analogies between some famous Kitsune and Set.
Taoki, the cat you're thinking of is probably Bast, who looks a lot like Anubis but is in fact a cat
She is often placed alongside Anubis, not really for any similarity in personality or function, but just because She was a very famous household goddess and still venerated by many today, as is Anubis.
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