Workaround Flash not allowing fullscreen from Javascript
Just give your flash movie 0.1% opacity (you will need to use wmode), and position it directly over the html buttons. The user clicks on the flash but sees the html. The actionscript code just tells the player to go fullscreen, and then calls some javascript using ExternalInterface. Bounty please!
You could use Haxe to create one single codebase that will translate to javascript as well as actionscript.
This means off course, that you would have to learn Haxe as well.
[EDIT]
A simpler approach might be to create a sprite sheet of all your images. This way you just have to import your sheet in css and set proper position of the sheet's viewport. And then you could also load the sprite sheet dynamically into flash.
The only thing your would have to take care of then is the correct positioning of the images within your sprite sheet.
You can NOT trigger full screen without user interaction to a flash component IE: mouse click on a button.
Even though, you have a click event in JavaScript it will not work as that click event will not be in the flash stack.
[EDIT]
One work around you can do is build your app in flex and use css to style the buttons.
Another work around. Create a layout swf in flex using css to style the buttons, and load and position the other swf inside it.
The work around will take a little setting up but then when you want to change the buttons you just have to change the css such as image source or colors or whatever you are changing.