I tried doing that too by downloading from the Adobe website and it didn't work. The easiest way seems to be first delete the apk you have. Then go to Google Play on your phone and to My Apps. Tab over to the All Apps tab and you should find Flash in there (along with every other app you ever installed, even if you uninstalled it). There you can access the Flash page and install it. Simply doing a search for Flash won't work since it's not officially supported in ICS.