To play back your content you use NetStream to attach to the video source. NS can send a stream from FMS in these formats (flv/f4v/mp4/etc):
http://help.adobe.com/en_US/flashmediaserver/techoverview/WS07865d390f ac8e1f-4c43d6e71321ec235dd-7fff.html#WS5b3ccc516d4fbf351e63e3d119ed944 a1a-7fe7
I would highly recommend using MP4 with H.264 as HTML5 can use this directly and support for it is wide. This means if you get rid of FMS you can progressively play them by simply pointing toward a file on a webserver, very little re-coding.
Now to play the video, StageVideo is the GPU accelerated library that can attach to a NetStream. Otherwise you can try a premade component. Some components implement NetStream and NetConnection themselves so consult their documentation. Or you can code your own using the basic Video Class.
I would recommend the advantages of GPU acceleration on devices with StageVideo but you must realize how it layers with Flash. It is not a display object on the display list. Just like Stage3D it exists below flash. The gratituous Getting Started with Stage Video article will show you a graphic of it and the basics of it. You will, however, need to create/program your own controls.
If you want to display a video in HTML5 the only thing you can do is use a StageWebView. This is opposite of StageVideo or Stage3D. A StageWebView sits over flash and is also not part of the display list. You cannot show any flash content over it, therefore you must rely on its own built in browser media player to provide controls for your video. It can natively play mp4 if you tell it to load it directly however it will be progressive playback. Someone else might want to chime in with any experiments with FMS and SWV. I play most of my videos in a StageWebView. Performance is GPU accelerated, I don't need to "hide" my entire interface, it comes with controls and fullscreen works.
No you can't use a Flash skin over a HTML5 <video> object. You must stop thinking iOS will allow you to run a SWF. When you are talking HTML5 you are talking about using StageWebView. All you can do is create a HTML5 webpage with your player re-created in javascript while injecting that website into a StageWebView. It's not advisable because you cannot affect the loaded page. There is no bridge in communication between AS<->JS like there is on the web. Maybe in the future. Until then there's almost nothing you can do (outside hijack location changes) to communicate between AS and SWV unless you use a native extension.
