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=11.3.31.323
Or, how about Use Pepper Flash Player From Google Chrome In Chromium Browser (linux)?
Note: Unlike Chromium, the similar Google Chrome browser includes Adobe Flash Player built-in. To view content with Flash Player in the Chromium open source web browser, install the Flash Player plug-in at /flashplayer. Apparently you have to install it, according to Adobe's Flash Player Help / Use Flash Player with Chromium page: