Adobe Flash Player 11.2.x is the last release available for Linux, future versions only being available through a new API called "Pepper" as part of Google Chrome. If you want to use the latest Flash Player 11.3.x in Linux, but with Chromium, not Google Chrome, here's what you must do.
1. Firstly, you'll have to download and install Google Chrome. Any version will do; in my test I've used Google Chrome unstable (23) and Chromium stable and unstable (21 and 23; PPA here).
2. Now, to launch Chromium browser with the Adobe Flash Player version bundled with Google Chrome, use the following command:
chromium-browser --ppapi-flash-path=/opt/google/chrome/PepperFlash/libpepflashplayer.so --ppapi-flash-version=188.8.131.523
Important note: if you don't use the "--ppapi-flash-version" flag, the Flash Player version reported in chrome://plugins will be wrong. You can find out what version to enter here by opening a file manager and pointing it to /opt/google/chrome/PepperFlash, then open the "manifest.json" file and you'll find out the Flash Player version number under "version" (it should be on line 4).
Now open a new tab and enter "chrome://plugins", and see if the Flash plugin version is correct. You can then check the Adobe Flash version you're using, here.
Update: an easy way to always have the correct Flash Player version in Chromium is to do the following. Open ~/.profile with a text editor:
And add the following line:
export PEPPER_FLASH_VERSION=$(grep '"version":' /opt/google/chrome/PepperFlash/manifest.json| grep -Po '(?<=version": ")(?:\d|\.)*')
3. Try it out and if Adobe Flash Player that comes bundled with Google Chrome is working fine for you in Chromium, let's make it permanent so you don't have to use any command line parameters in the future.
For this, you need to open the /etc/chromium-browser/default file as root with a text editor:
And replace CHROMIUM_FLAGS="" with the following:
gksu gedit /etc/chromium-browser/default
This will automatically get the Flash Player version from the Google Chrome manifest file once you log out and log back in.
Arch Linux users can install THIS package via AUR instead of following the instructions above.
info via ubuntuforums; thanks to Gregory Kramida for Flash version tweak.