How do I extend existing 10/3 wiring to run a compressor that needs 12/2 wiring?
A simple solution would be a specialty extension cord like this:



It's hard to see from this pic, but it's a 240 v Male, with several 120v outlets on the other end.  You could plug it in where the kiln is, thus ensuring both can't be used at the same time.

Made by Ericson.  But the low end one is $350.  You might be better off to run a new circuit.