IMHO, Flash is on its way out, although it would be an exaggeration to say it's on its deathbed. Flash is incredibly inefficient. A good way to lose an hour of battery life on your laptop is just leave open a few websites that make use of Flash (even seemingly innocuous uses). The iPhone/iPad incompatibility issues (and the subsequent Thoughts on Flash commentary by Steve Jobs) have done a lot to bring this topic to the attention of the general public. Some of it is FUD, but there are good points there, and in any case, the average iPhone user is more than willing to believe The Steve.

Google is already moving away from using Flash on Youtube; HTML5 works on most videos (those without ads) on most platforms and browsers. Facebook is heavily encouraging its app developers to use HTML5, and according to my cursory Google search of "facebook flash"...it's been a while since someone wrote a tutorial website on developing flash apps for Facebook.

Simply put, Flash is not seen as desirable by a lot of people. It is hanging on simply by momentum but a lot of that is getting sapped by the moves of these big game-changing companies.

If Flash is still needed in the future for whatever, you can use Chrome. Opening up an alternate browser once in a while doesn't seem like a big deal for me; I remember having to use Internet Explorer as an alternative to Firefox for things like banking for a couple years until finally everyone caught on and now Firefox is the standard. At least you can get Chrome for Linux (unlike Internet Explorer).