Adapted from instructions by Bodhi's lead developer, Jeff.
To manually install flash:
1. Download the tar.gz version of libflashplayer.so from here.
2. Place the file in /home/<username>/.mozilla/plugins.
3. Restart all instances of Firefox. Firefox is ready to use Flash.
To ensure that Firefox has fully restarted, you can log out of your session and log back in.
If the procedure isn't working for you, ensure that all your spelling and capitalization is correct. For example, “plugin” instead of “plugins”.