Nintendo has confirmed that the NetFront powered browser for their upcoming Wii U console isn't compatible with Flash, and no other plug-in (Google Earth, Java, etc.) for that matter.
To make matters worst, the browser won't allow you to download/upload images nor video; however, the browser is capable of playing some MP4 and M3U8+TS (HTTPLiveStreaming) videos on the web.
Here's a Japanese demonstration of the Wii U's browser:
Image Credit: Nintendo