The thing is, facebook does not need the latest flash, it intentionally shuts you out, even though all the necessary functionality is there. This app works around that.

The app should be avaiable through the Application Manager (note it has just been promoted, so depending on caches, etc it might take a few minutes/hours before everybody sees it around the globe).

Start it, pick the recommended version of Flash and tap "change". That's all there is to it.