That is a very broad question, one that html5 may not be able to resolve--you might have to wait until it is an officially released language and is more fully supported to find out what its limitations are. Even then I doubt there will be any way of converting from Flash to html5. Flash involves programmed/compiled files, while html5 is merely a markup language implemented in ascii text files.
You will have to learn html5 from the ground up and then learn how to design things with it (and probably various other languages) to get the equivalent of what a Flash file can provide on its own. It is quite possible you won't be able to produce some things that Flash can. Flash has capabilities that I believe html5 alone simply will not likely be able to match.
Adobe has officially released the Flash to HTML5 converter named Wallaby. It is already downloadable for Developers to download from Adobe Labs website. Besides, Moyea SWF Decompiler is a professional SWF Decompiler that supports flash components and can easily extract flash components like images, sounds (mp3, wav), videos (flv), fonts, buttons, and even action scripts, etc. Maybe Moyea SWF Decompiler can help you .
It depends of what you have to do.
For my part, banners and stuff alike would be manageable with conversion softwares like Adobe's.
But if I would do an app for a client, I wouldn't want to put my neck and reputation on the line, for those very reasons Ned answered. I always have the mentality of programming in the native langage instead of relying on converter.
You can try with Wallaby from Adobe (http://mx.ibtimes.com/articles/10755/20110308/adobe-flash-convertir-ar chivos-fla-html-apple.htm ) but it has some restrictions of what you can really export (http://labs.adobe.com/wiki/index.php/Wallaby#Installer)