Can I fire a 240-volt, single-phase kiln in a building that has 3-phase, 240 volts?

Yes, you can run your single-phase, 240-volt kiln on a 3-phase, 240-volt system. You do not need to rewire your kiln. There is a possibility that a phase can be out of balance by running a single-phase kiln in the building. To be sure, you might want to talk to an electrician.