Eric, thanks for your help anyway.
For what it's worth, I just installed KDS 3.2.0 on Mac OS X, plugged in the FRDM-K22F with the same JLink_OpenSDA_V2_1_2015-10-13.bin firmware, and got the same error:
J-Link GDB Server failed:
Unknown error. Please use J-Link software v4.96f or later.
For more details, see the JLinkGDBServerCL console.
This Mac never had KDS installed, so this isn't about leftover files.
Has anybody actually tested this configuration? Is this a supported combination?
On a more general note — I use Kinetis processors in my designs, but there is an increasingly troublesome "Kinetis tax". Every couple of months I'm spending considerable time updating KDS or its components, updating the KSDK, learning about the changes, reading the release notes, trying to follow the (sometimes strange) instructions on fixing problems, encountering problems like the one described above, searching the net for solutions, asking questions, detailing configurations, trying out various combinations of files and versions. This engineering time lost is beginning to be noticeable as a considerable cost of using the NXP/Freescale Kinetis line.