If the Adobe blog post is correct and the pepper plugin is only distributed with Chrome and isn't open source and part of Chromium then how is another browser going to support it? They'd have to tell you to install Chrome and then open the plugin from within Chrome's installed directory. Pretty ugly solution.
If it's open source and part of Chromium then they can at least take the source out and ship their own, assuming the licensing allows for that and is compatible with their license.
All in all, this sounds like a pretty complex scenario for non-Chrome browser.
Not Chrome, they can't it is not open source. They could switch to Chromium, which could presumably run flash, but it is not clear how you obtain it if only Chrome will distribute it. Presumably they will have to distribute it as they say they will ship security updates, but that is unclear, as Linux flash does not auto update from Adobe.