It just doesn't quite work out of the box.
First, a flash object within an HTML form element fails when the flash runtime tries to register the callbacks you defined in your Flex app (e.g. a callback added in ActionScript using ExternalInterface.addCallback("someFunction", someFunctionPointer) is evaluated in the browser as __flash__addCallback(objectId, "someFunction"). A hack to get around this would be to assign your Flash object to window.objectId as soon as you've created it: hey presto! you've worked around one limitation.