Everyone is saying that flash design is dead for websites. Besides the issue of compatibility with "iDevices", why else should flash be kicked out the designer's door?
I've edited your question so that it's not as vague/subjective.
HTML5 doesn't really replace any particular aspect of Flash in that HTML5 is simply and updated spec for HTML.
Those in combination can do a lot of the things that we had to rely on Flash in the past for.
Where you really don't need to use Flash anymore include:
Where you may still need flash would be for complex interactions such as gaming, though, in time, much of that will go the way of native support in the HTML5 package as well.
Rumors of Flash's death are greatly exaggerated, but whether you personally should toss it depends on your market, the kind of work you're looking to do, how well you know Flash as an authoring tool, and your clients. The answer that's right for you depends on all these. This answer will be a bit long, because there's perspective involved (as a fogey, I get to have more perspective -- one of the advantages of fogeyhood) and at least one controversial prediction.
Consider, too, that the CSS3 spec is a l-o-n-g way from being complete at this point. I have one (XHTML) client site I'm dying to switch to HTML5, but looking at the visitor browser specs, I don't dare. Most people aren't going to switch to Chrome just so a site will look good; they'll just go somewhere else.
So why would Flash survive? Because a lot of big commercial sites will need it. Hollywood, to take one example, has to be able to build rich interactive sites quickly and know that the user experience will be the same across browsers. iThings aside (they are still a tiny percentage of web visitors overall), there's just too much that you can't rely on with HTML5 as yet. It's not a matter of a quick shim to cope with IE6 any more. It's four major browsers in various versions plus a couple minor ones all supporting different parts of the draft standards, all changing with each new release, and you still need a shim to cope with IE6. Flash has the huge commercial advantage of being a constant, and a rapid development environment -- both important if your livelihood depends on time-to-market.
In the same time frame as HTM5/CSS3 standardization, web-based applications and cross-platform/cross-device apps that use the web will become way more important; users love them and our clients will have to provide. Where we used to build websites, we'll be building the web and mobile apps that will replace them. Think of apps as the small furry animals scurrying under the feet of huge website dinosaurs, destined to take over the world. Flash and Air definitely have a place in that landscape, so regardless of the final output format, Flash looks to me like it will remain a viable authoring tool.
I highly recommend watching the full video of the Day 2 keynote from last week at MAX. It gives a pretty good overview of where HTML, js, Flash, etc., stand and where Adobe is going with all of these technologies.