After many years animating and programming in Flash, it seems that this tool will disappear from the web in favor of HTML5 (only from the web, because i continue using it for desktop applications and more). One reason is the refusal of Apple to support Flash on mobile devices, and since these devices are increasingly used to navigate, we must stop using it for web development.
So to make animations that can be seen on the iPhone / iPad, no choice but to make HTML5.
Right now there are several ways to convert Flash to HTML5:
This tool from Adobe, still in beta, imports directly the "fla" sources and turns them into HTML5 (generates several files, including graphics in SVG format).
The problem is that it is very limited, at least in this beta. Only allows very basic animation: Alpha, buttons, Actionscript (well, the stop() does work) and not much more.
This Google tool is a surprise, importing "swf" files (must be generated to support Flash Player 8 - Actionscript 2) generates HTML5 with a good chance. Unlike the Wallaby, it does allow buttons, alpha, basic Actionscript and many more.
The swf is converted into 2 files, an HTML and a "runtime.js".
All the tests I've done have been good, they were perfectly in both the iPhone's Safari and as an app with a UIWebView. In fact the samples gallery that provides Swiffy is good enough to see its potential.
For now HTML5 creation editors are very poor (see what will happen with Adobe Edge), so we will have to continue converting Flash to HTML5.