I think you would need a KCA-S220 switch. Head unit to switch, port 1 of switch to phatbox, port 2 of switch to BT200, feedthru on BT200 to sir-ken1 *or* port 1 of switch to sir-ken1, feedthru on sir-ken1 to phatbox, port 2 to BT200. I would try the first config first.
Of course, you also need the proper Kenwood to Keg cable and to apply the kenwood firmware to the keg if it is not already set up for it.
Jeff