Thank you for your post.
The WebViewer is not a browser. FileMaker Pro uses the built-in OS webkit (Safari for Mac OS and iOS, Internet Explorer for Windows) to display web pages in the Web Viewer. If there is HTML 5 being used, it is coming from the built-in webkit; not FileMaker Pro. There are definitely differences between what the webkit can display and what a browser can display.
I have seen Flash pages in a Web Viewer, so these should display.