The flagstone is the heaviest part, and definitely heavy enough to leave it somewhere fairly permanent. I keep it out in the shade where it can get rainwater, and in the summer the stone under the roots should stay cool.
It would be fun to find a way to incorporate more stone for indoor plants. I always end up with tons of flies over my indoor seed trays, and then I remember adding sand and decorative stone on top works to prevent them from reproducing. Having real stone surfaces on table furniture for plants would look and feel awesome, but that would be super heavy when moving.