Greetings
I presently have 3 distros installed on my main PC (several others on various boxes) and at least on 2 of them Firefox reported, when using "Help/About_Firefox/Check for Updates" on v15, said no updates were available. I looked manually and found v25, installed it and went about the process of checking addon updates.

I updated Java and the rest and when I got to Flash, Adobe page said
"NOTE: Adobe Flash Player 11.2, the last version to target Linux as a supported platform, requires Firefox version 17.0 or higher. " Bold was added by me.

So does anyone know if
1) Adobe is indeed dropping support for Linux?, or...
2) Is HTML5 far enough along to supplant it?

Google has a monopoly on the Linux Flash player now. Flash players newer than 11.2 (for Linux) are developed by Google and bundled with Chrome.

See:

Adobe roadmap for the Flash runtimes

In a word, no. Here's a thread about one of the political issues involved:

The fight for HTML5: 'Keep DRM out

Not entirely (yet). For now they "outsourced" Flash to Google. Which is a dastardly deed from Google since they are the only ones that supply the latest versions. But as Flash isnt available on Apple IOS and Android and web content creators who want everyone to be able to access their sites and videos probably begin to ditch flash sooner or later. So Flash in its present form may be in its way out already.

For you or for the world?
I assume most stuff Flash does can be done with Javascript/Html5 but i imagine it can be quite complicated right now.
But this isnt that important for the end user - the important thing is that Flash is here and will be for the foreseeable future, albeit i dont know for how long will be essential for a good browsing experience.

And as for the topic title, the Linux web support is just fine.