<<Disclaimer: Verify this information before applying it to your situation.>>

Thank you to all those who responded to my question.

There were two ideas.

1.  It will be OK to just put two cups of rice through the mill and
throw it out.  This is Whisper Mill's recommended cleaning method,
apparently.

2.  It will not be OK to just throw out grain, especially if I am
extremely sensitive.  In that case, blow it out with compressed air.

FYI, my sister, also a celiac, has a magic mill.  She took it apart and
cleaned it herself, and from her description just putting a few cups of
rice through would not work for the magic mill.  I tried to take my
Whisper Mill apart similarly, but could not get at the mill assembly.  A
few kernels of wheat fell out during this process, but not much flour.

I've opted for the first idea.

Christopher Tyler
St. Paul, MN