The firefox version 22.214.171.124 will not take flash 10. However, it will work with flash-player-plugin-126.96.36.199 with some limitations on some sites. That is if you can find it. (i.e. no NGC video, enlarment screens, Hulu, yahoo video on popurl or metacafe site).
To install the plugin it goes in /usr/lib/mozilla-firefox/plugins/ file. Or locate similar file. Or ~/.mozilla maybe a last resort.
hth && gl
If you want the old flash9 plugin I've uploaded it here