Flash isn't dead yet. While most mobile webpages no longer use it, on the desktop you still see it pretty frequently. As for its impending death, that has been a long while coming:
* using Flash to design a whole website became mostly unnecessary due to HTML/CSS becoming more powerful
* using Flash for vector animation became replaced by regular video and Youtube
* using Flash as video player became unnecessary due to HTML gaining a <video> tag
I am not quite sure what happened with Flash and gaming, Newgrounds.com is still around, but you rarely hear about it anymore. Doing games in HTML with <canvas> and WebGL is now possible as well, but I don't really see those very often. I assume Unity and mobile gaming took mostly over what was once done in Flash.
However what really killed Flash was Adobe no longer supporting it. When software is full of security and performance issues, it's no surprise that people will move away from it. Flash got popular in the first place because it did things that your browser wouldn't be able to do on it's own. But while browsers got more powerful, Flash just sat there and didn't really improve much at all.