This article outlines your speculation about stock browser differences between manufacturers, that absolutely is true: 5 reality checks every team needs before working on Android webkit
…which does cause trouble and mysterious/difficult to diagnose/solve problems.
As far as your issues with your WebView
implementation:
Version of jquery-mobile
may be an issue jquery-mobile loaded into an android WebView if you are using jquery.mobile-1.0.1.min.js
you may want to try the uncompressed jquery.mobile-1.0.1.js
And Flash :-/ Good luck:
Screen blinking when using a webview with flash
Flash in WebView not working on Android 3.2
Flash video not displaying in WebView for Android 3.0.1
For loading SWF:
loading flash files (.swf) webview in android
Good luck with that, seems like a lot of variables with devices, Android versions, etc. And will take persistence with trial/error.