You can only call JS functions from the page the swf object is embedded in.
Considering AIR aps are not webpage-embedded, you cannot call JS functions in the same way.
To use the Clipboard capabilites, you need to use the Clipboard class in Flex.
Just do a google on that and you'll find the answer you need with code and all.
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SET CLIPBOARD DATA:
var textToCopy:String = "Copy to clipboard.";
Clipboard.generalClipboard.setData(ClipboardFormats.TEXT_FORMAT, textToCopy, false);
GET CLIPBOARD DATA:
var text:String = Clipboard.generalClipboard.getData(ClipboardFormats.TEXT_FORMAT);
Thx is working with Flash Player 9. But I'm afraid that won't be working with FlashPlayer10 (i mean, with rollOver in flashplayer10).
I think it will work, but if it doesn't you should look in the LiveDocs for Flex 4 / FP10.