He had a particular good pass on December 20th and obtained a very nice video record, tracking on the satellite with a motorized mount (note: movie has a period of black screen between opening title and start of the video record):
The satellite is the object near the center of the screen, flashing about each 8.5 seconds with periods of invisibility inbetween. The moving streaks are stars (the mount is tracking the satellite as it moved along the sky): the other stationary dots in the image are hot pixels on the sensor of the video camera.
The video allows for an analysis of the flashing behaviour of the satellite. I used LiMovie to measure the satellites' brightness on the frames, resulting in the following lightcurve:
Visible is a clear ~8.45s periodicity with flashes of a specular character (suggesting a flat reflective surface). I have marked this with red triangles 8.45 seconds apart. In between the main flashes, a pattern of smaller secondary flashes can be discerned in a semi 8.45 second peridicity too (green triangles). They are not exactly positioned halfway between major flashes.
Assuming that each major flash is a flash caused by one of the sides of the KMS 3-2 cube-shaped body, then it completes a tumble once every ~33.8 seconds. Assuming that the less clear secondary flashes are due to a side of the cube as well, the tumbling periodicity would be half of that, i.e. 16.9 seconds.
Greg recorded the UNHA-3 r/b from the launch too. That one too is tumbling:
Again, I used LiMovie to extract brightness information from each video frame. That was less successful with this video, because Greg's mount had difficulty keeping up with the fast-moving r/b for much of the record. A considerable part of the video could not be used for analysis, and I had to chop up the analysis in little non-continuous chunks:
What can be seen, is a flashing behaviour that starts slow and gentle and is increasing in rapidity near the end of the analysis, this being an effect of changing viewing angle.
Contrary to what some alarmist (sometimes almost hysterical) media reports have suggested, the tumbling of KMS 3-2 is by no means dangerous. David Wright over at All Things Nuclear has a very good debunking story about this all, pointing out the many misconceptions rampant in the reporting.