I am having the exact same problem. When Flash could not be upgraded on my 10.8 computer I was suggested by Adobe's site to uninstall the previous version. So I did and now I have no Flash at all and cannot install it either. Exact same log lines ("Non-OS Volume detected") when I run the .pkg installer. Very frustrating.
Had my brother send me the actual Flash plug-in file, dropped it into /Library/Internet Plug-Ins, and voila, it worked fine. So this is an installer issue, and for me it doesn't matter if I use Adobe's fancy AIR-based installer or their .pkg. Their Flash installers simply do not work on my OS X 10.8 computer.
Here is the plug-in zip if anyone else is having the same problems: https://dl.dropboxusercontent.com/u/1723805/Flash%20Player.plugin.zip
Just unzip and move to /Library/Internet Plug-Ins
If Adobe objects to me publishing it, I'll remove it.
Uh. Weird. I don't even have that "flashplayer.xpt" file. Yet Flash seems to work fine on all sites I've visited today. Does anyone have any idea what it actually does?