I had an android 4.0 Ice Cream Sandwich tablet and it's integrated flash into browser worked great! It's really smart -- works with clicks on internal buttons and the video performance worked perfectly!
But then I got a Google Nexus 7 with Android 4.1 Jelly Bean and lo and behold .... no built in flash. I did my research and saw that Adobe has had trouble getting support from mobile developers Google and Apple, and have recently thrown in the towel and have decided to stop making future Flash mobile versions (except for security updates for existing users).
So google dropped support for existing flash on new devices and won't let users install it from Google Play. Adobe made a statement about it in the header description.
Fortunately, there are hacks and work arounds which I have done for my Nexus 7 / Firefox Beta and, thank God, it works beatifully.
Google's statement to users? Switch to sites that use HTML 5. But my statement to Adobe ... are you going to let this happen? Especially as Windows 8 Tablet is set to hit the market and more and more people are switching from laptops to tablets? Flash is already losing it's relevance on the web.
Flash Android already works fantastically! Just keep it up to date. Let Google nix it on Chrome and keep it working on Firefox. How much trouble could that be? You've already made the investment. Just keep flash relevant.