With LPC-Link2 and CMSIS-DAP (LinkServer) firmware and MCUXPresso IDE, it supports both Kinetis and LPC devices.
KDS has some very (very) basic support for CMSIS-DAP, and I don't recommend that combination.
Anyway, I recommend using the MCUXpresso IDE, as this has replaced KDS and MCUXpresso has many more and better features plus supports more probes including the LPC-Link2.
I hope this helps,
Erich