I found something that says Google's Chrome Browser should do the job (using a 'pepper-based version'), and for Chromium there is an ppa. Some search on the web like 'Ubuntu Adobe Flash 15' or similar does not return any good websites.
Adobe will continue to provide security backports to Flash Player 11.2 for Linux. NOTE: Adobe Flash Player 11.2 will be the last version to target Linux as a supported platform. Some application seem only to be running with Adobe Flash 15 (or at least I know it does, because I have that version on my Windows Partition).
I know, it's been asked before but I couldn't really get a satisfying answer for some details/backgrounds and I guess it's an important question for many.