If you want to use ExternalInterface to enable Flash-to-JavaScript and JavaScript-to-Flash communication, you'll have to configure the HTML so that the allowScriptAccess parameter (<object> tag) and attribute (<embed> tag) is set to always. The default HTML published by Flash assigns a value of sameDomain to allowScriptAccess, so if you've published the HTML from Flash, you'll need to edit it. The following illustrates where you can locate the allowScriptAccess parameter and attribute:
<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" ¬
codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/ ¬
flash/swflash.cab#version=8,0,0,0" width="550" height="400" ¬
id="Example" align="middle">
<param name="allowScriptAccess" value="always" />
<param name="movie" value="Example.swf" />
<param name="quality" value="high" />
<param name="bgcolor" value="#ffffff" />
<embed src="Example.swf" quality="high" bgcolor="#ffffff" ¬
width="550" height="400" name="Example" align="middle" ¬
allowScriptAccess="always" type="application/x-shockwave-flash" ¬
pluginspage="http://www.macromedia.com/go/getflashplayer" />
</object>