If you look under Tools | Options | Projects | Amethyst you'll see two Web Browser properties. By befault these are set to IE and Firefox. You can switch between them dynamically by choing Amethyst from the main menu and right clicking 'Use Seconadry Browser' (it toggles).
However, the 'browser' in these properties can be any executable, so try setting the primary browser (say) to 'C:\Program Files\Flex 3 SDK\bin\adl.exe' (on my machine). Then when you try to debug, the IDE program launch will use ADL to run the program and not IE. So using the Flash IDE as the compiler will produce an AIR SWF file which you can then use to ADL to run. Also, that technique should enable you to use the internal Flash player to run Flash SWFs.
I tried to switch from IE to the Flash player (that's inside the installtion folder of Flash inside the folder called Players) and even though Visual studio is able to run it when I press F5 my swf doesn't get loaded.
I try to run the flash player from the shell passing the swf file as paramenter and it loads that correctly.
Am I missing something?