Just plug the kegerator's 120V cord into the Inkbird outlet. If you're worried the kegerator will "override" and cycle it off at the wrong time, just keep the kegerator's temp knob cranked all the way up to maximum cooling. Then it will only cycle when the Inkbird tells it to, based on your settings against actual temps sensed by the probe.
Be sure to set the compressor delay on the Inkbird to several minutes, so it doesn't cycle on/off too quickly.