In a small WebView app I wrote, I am able to load YouTube and see the picture the represents a video clip, with the familiar right-pointing arrow that is supposed to start p
Youtube got a HTML5 version, which means you can watch their videos without having flash installed. So better check flash suppport on a site where you can be sure that only flash is being used, eg http://www.adobe.com/software/flash/about/ which also tells you what version of flash you got installed.
Could it be a problem related to Javascript not being enabled on the webview?
myWebView.getSettings().setJavaScriptEnabled(true);
The Adobe Flash plugin is available from the Android Market for Android 2.2+ devices. It may come pre-installed on a few devices, but on most it does not.
Search for "Adobe Flash" in the Android market to download it, then try running your app again.