I ran into this on an old Thinkpad R31 -- Chrome's Pepper Flash doesn't show up, and the standard Flash 11 plugin crashes. I'm thinking it's related to old video cards, rather than the 32 bit system.
The official requirements for Flash 11 call for 128MB video RAM; my R31 has 64. I was able to download an old version (10.3) and it works, albeit with Chrome complaining about the old version.
Old Flash versions
. I used 10.3.183.23
. Extract /fp_10.3.183.23_archive/10.3.183.23/flashplayer_10_3r183_23_linux.tar.gz then extract libflashplayer.so from that and put it in /usr/lib/mozilla/plugins. Chrome will pick it up there.
To keep Chrome from complaining about the old plugin, you can modify the launcher to include --allow-outdated-plugins
Edit: I also tried 11.1 and that works too. However, performance with both are pretty bad.