I only recently discovered this myself (and admit I haven't used it yet) but if you already have a lot of content in HTML you might look at http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/flash/html/HTMLLoader.h tml
I would assume so because the only reference to iOS on that page is:
softKeyboardInputAreaOfInterest : Rectangle
Defines the area that should remain on-screen when a soft keyboard is displayed (not available on iOS).
I am not sure they would go out of their way to specify a single variable as not available on iOS if the entire feature didn't work.
Alternatively, if you want to keep the whole page in HTML you might also look at PhoneGap: http://phonegap.com/
It's 100% free and Adobe recently bought it.
Well it does say... "But is not supported on mobile devices..."
There is also something called stagewebview that seems to be the same thing but does say it supports mobile.