The "20 pin" interface you show is the older 0.100" spaced one.
The "19 pin interface is what is used on Kinetis. It's really a 20 pin with one pin removed.
The 19 pin is 0.050" spaced pins and is much smaller. You will need an adapter if you are plugging into the older "BIG" 20 pin JTAG
In addition to this there is a smaller 9 pin version.
You can see them here:
http://www.segger.com/jlink-adapters.html
look up
- J-Link 19-pin Cortex-M Adapter
- J-Link 9-pin Cortex-M Adapter