I managed to get flash and java applets working on my Backtrack 5 R2 KDE 64bit on Thinkpad T420 laptop I'll describe what I did:
1) For firefox flash plugin, go to http://get.adobe.com/flashplayer/otherversions/ and choose Linux(32 bit) as operating system, tar.gz version of the installation package, and download the tar.gz file. Download it to a temporary folder that you create (eg /root/flash_install_kit), unpack it and copy the libflashplayer.so file to a location where firefox looks for plugins. Here's how the commands sequence should be (commands executed as root or with sudo):
Now restart firefox and your flash should be working, check in Tools -> Addons -> Plugins and ... check youtube.
~# cd /root/flash_install_kit
~# tar xzvf install_flash_player_11_linux.i386.tar.gz
~# mkdir -p /usr/lib/mozilla/plugins/
~# cp libflashplayer.so /usr/lib/mozilla/plugins/
NOTE: choose 32 bit version of the Flash Player even if your BT is 64bit, I noticed that at least Firefox 14 cannot use the 64bit version of the flash..
2) For enabling Java applets, install icedtea-6-plugin, the description is clear:
Now, a note on Java: Firefox on BT5 comes with NoScript extension enabled and configured to block Java applets. To workaround this, you have some options: either find a way to configure NoScript to allow Java (I couldn't figure it out), or disable NoScript (not recommended, in my opinion), or...install a second browser(I installed Chromium, so I'll just write my approach).
icedtea-6-plugin - web browser plugin based on OpenJDK and IcedTea to execute Java applets
Now start Chromium (btw, to run the Chromium the BT-way, ie as root, call it from terminal like this "chromium-browser --user-data-dir /opt/chrom/"), and your Java applet plugin should be loaded and working. You can test if Java works for you at this link: http://www.java.com/en/download/testjava.jsp
~# apt-get install icedtea-6-plugin
~# apt-get install chromium-browser
That's it. Hope it helps..