Note that it does make a difference if you are using a 32bit or 64bit OS. There is no 64bit debugger for Linux (thanks Adobe!!) so to get it to run you have to do something like the following script. I've taken this from sites online so I'm not sure who the original author is. There are some credits listed. I take no credit myself
Basically, AFAIK, Chrome will use the plugin from Firefox. This script will remove anything that is existing, install the dependencies such as nspluginwrapper (to make the 32 bit plugin work on 64 bit) and ia32-libs which are also necessary, then redownload the debugger plugin and install it
I think now that Chrome bundles Flash Player you have to go into about:plugins and disable the integrated debugger. See here for more info on that: http://kb2.adobe.com/cps/839/cpsid_83950.html
#!/bin/bash
# Script created by
# Romeo-Adrian Cioaba romeo.cioaba@spotonearth.com
# Super minor updates by jason.melton[at]gmail[dot]com
# Released under GPL
echo "Stopping any Firefox that might be running"
sudo killall -9 firefox
echo "Removing any other flash plugin previously installed:"
sudo apt-get remove -y --purge flashplugin-nonfree gnash gnash-common mozilla-plugin-gnash swfdec-mozilla libflashsupport nspluginwrapper
sudo rm -f /usr/lib/mozilla/plugins/*flash*
sudo rm -f ~/.mozilla/plugins/*flash*
sudo rm -f /usr/lib/firefox/plugins/*flash*
sudo rm -f /usr/lib/firefox-addons/plugins/*flash*
sudo rm -rfd /usr/lib/nspluginwrapper
echo "Installing ia32-libs and nspluginwrapper"
sudo apt-get install ia32-libs nspluginwrapper
echo "Getting libs"
sudo getlibs -p libcurl3
sudo getlibs -p libnss3-1d
sudo getlibs -p libnspr4-0d
echo "Installing Flash Player 10"
cd /tmp
wget http://download.macromedia.com/pub/flashplayer/updaters/10/flashplayer_10_plugin_debug.tar.gz
tar zxvf flashplayer_10_plugin_debug.tar.gz
sudo cp libflashplayer.so /usr/lib/mozilla/plugins/
sudo chmod +rx /usr/lib/mozilla/plugins/libflashplayer.so
sudo nspluginwrapper -i /usr/lib/mozilla/plugins/libflashplayer.so
echo "Linking the libraries so Firefox can find it."
sudo ln -sf /usr/lib/nspluginwrapper/plugins/npwrapper.libflashplayer.so /usr/lib/mozilla/plugins/
sudo ln -sf /usr/lib/nspluginwrapper/plugins/npwrapper.libflashplayer.so /usr/lib/firefox-addons/plugins/
echo "Done :-)"