How-to: Flash Player 10 for 64-bit Linux ( in 4 easy steps )
Adobe’s newly released 64bit flash plugin for Firefox running on GNU+Linux makes installation on 64-bit operating systems a walk in the park ( like I said – 4 easy steps )
- Download the plugin from http://labs.adobe.com/downloads/flashplayer10_64bit.html . Direct download link
- Extract libflashplayer.so from the downloaded file
- copy libflashplayer.so to /home/<username>/.mozilla/plugins/
- restart Firefox !

Google Chrome too takes its plugins from the .mozilla/plugins dir, so essentially this also works for Google Chrome[ tested by me
], and to make it system-wide, put it in /usr/lib64/mozilla/plugins/