This post could help with what you want: SWD Debugging with the FRDM-KL25Z Board | MCU on Eclipse
To use KL25Z as programmer/debugger you have to isolate the KL20x OpenSDA programmer from the KL25 target. Connect the SWD header to another target SWD and should (perhaps you'll need to change the firmware from FRDM board, MCU on Eclipse has some posts about that).
Just a remainder NXP support for the KE0x sub-family are quite weak, I've been struggling to get an KE02 self-made development board to work.
KDS doesn't come with KE0x driver library, but you can find then here: https://community.nxp.com/docs/DOC-329476
Nevertheless, I would suggest you considering an LPC, like LPC800, they have similar prices, TSSOP packaging.