I wouldn't bother with the GFCI. If the kiln has no timer or other device requiring 120v, then the 3 wires go as you stated, one hot on each phase through a double pull breaker and the ground wire to the ground buss.
However, the new panel should be tied to the main with an isolated ground.
Please read this for a complete explanation of how a sub panel is to be installed:
Definition of Subpanel Ground/Neutral Isolation [Archive] - The Garage Journal Board