Hello,
you have a typo - missing "S" after word USER. Correct version is below:
export ALLUSERPROFILE=/tmp/pex
./kinetis-design-studio
I just verified it works with KDS 3.2.0. The directory in the env. variable is automatically created (if pointed to the place where the user has the appropriate rights.
It is also visible in the Processor Expert console:

Hope it helps,
Libor