Google's gallery includes two ads and two simple games that look pretty well when converted to HTML5, especially when you're using Chrome.
Swiffy uses some SVG features that are only available in WebKit browsers, so that's the reason why you can only use it in Chrome and Safari. Android's browser for smartphones doesn't support SVG and it's likely that the Android 3 implementation doesn't support the required features.
"A SWF file is converted in two phases: the Swiffy compiler (which you can use on this website) processes the SWF file and generates a JSON file. A client-side JavaScript runtime loads that JSON file and renders it using HTML, SVG and CSS. Swiffy supports many common SWF features such as vector graphics, embedded fonts, images and timeline animation. Basic ActionScript 2.0 code is also supported, but don't expect to convert your favorite Flash game yet. In general, Swiffy supports most of the features in Flash 5, so exporting your file as a Flash 5 will give the best results," explains Google.
Unfortunately, the code generated by Google is difficult to edit, so you still have to go back to the original Flash file. Adobe has its own tool for converting FLA files to HTML5.