As you may know, Mozilla decided to disable Adobe Flash on its Firefox browser, due to the critical security flaws discovered in the platform. But Adobe has announced that an update is on its way, being scheduled for release this week.
Mozilla is also testing Shumway, a HTML5 renderer for the SWF format used as a flash replacement.
The latest version available is Firefox 39, which has been recently released. To install Firefox 39 on all the major Linux systems, see the instructions here. For Ubuntu, the latest versions of Firefox are available via the default repositories, so installing it is quite easy (instructions here).