Q:

How to access Flash ExternalInterface from QWebView? 

Is it possible to access Flash's ExternalInterface from QWebView?  If so, how can it be done? 

A:

You could try accessing it via executing JavaScript in the page. 
To run JavaScript on the page use QWebFrame::evaluateJavaScript, for example:
QWebView* webView;
// ...
QString jsQuery("document.getElementById(\"flashobj\").flashFunc(1);");
QVariant result = webView->page()->mainFrame()->evaluateJavaScript(jsQuery);

Note: I've not tested this code, or even tried accessing Flash before via QtWebKit so this may not work for Flash, although it does work for JavaScript objects.