Statement from the writer
A fan theory1 claims that the amniomorphic spell creates pots, based on the alternate etymology below. Since Starswirl has a beard, he is “hairy,” and since he invented a spell for making pots, he is a potter: a hairy potter. This would make the spell a <PERSON> joke.
From this interview2 with <PERSON>, the writer of that episode, he denies that the name of the spell was intended to be a <PERSON> joke, although he likes the idea. 817
He didn’t state any source for the origin of the word.
If we accept his joking agreement as a retcon, then the amniomorphic spell creates pots.
Straightforward etymology
Without a definitive statement from the author, we can look at the etymology of amniomorphic.
All English words that start with amnio- relate to the amnion, a membrane surrounding an embryo.
Definition of -morphic from the Oxford English Dictionary:
-morphic: Forming adjectives with the sense ‘having a form or character denoted or described by the first element of the compound’.
A straightforward reading of the word would be, “having the form or character of an amnion.”
Alternate etymology
Someone named <PERSON> decided to dig deeper into the prefix amnio-, trying to find other possible meanings.
Etymology of amnion from the Oxford English Dictionary:
amnion: Greek ἀμνίον the caul, diminutive of ἀμνός lamb.
Etymology from the Online Etymology Dictionary4:
amnion: Modern Latin, from Greek amnion “membrane around a fetus,” said to be originally “bowl in which the blood of victims was caught” [<PERSON> & <PERSON>], which is variously said to be of unknown origin, from ame “bucket,” or a diminutive of amnos “lamb.”
Conclusion
From the etymology, the word presumably means something like, “related to the form or character of an amnion, a lamb, or some type of bowl or bucket.” An anmiomorphic spell could do anything from turning something into a bucket to making someone sheepish (the character of a lamb). In any case, it wasn’t an intentional reference to <PERSON>. It’s entirely possible that the writer just made the word up, without considering its etymology or deciding what the spell was meant to do.
1 Claim about being a <PERSON> joke is here. Link provided by <PERSON>
2 Link provided by <PERSON>
3 Link provided by <PERSON>
4 Link provided by <PERSON> 817