Since I'm running Ubuntu, I decided to try the 'download for Ubuntu' option on the download form. It went down like this: - Firefox asked me whether I wanted to launch the 'apturl' tool. I accepted its suggestion. - I got a dialog saying "This will enable the Canonical Partners repository". I'm pretty sure I already had it enabled, but sure, what the hell. - I got the usual 'downloading updated package lists' dialog.…
I did backup the old plugin though, just in case.
I also tried just updating Chrome, which is supposed to have the newer flash version, but it didn't have it. Not sure why..