Upcoming Android 4.1 Jelly Bean devices, starting with Google's recently unveiled Nexus 7 tablet, will not receive official Flash Player support from Adobe. Moreover, Adobe announced plans to pull Flash Player from the Google Play Store on August 15 for unsupported devices, and while you can expect Flash updates to roll out for older hardware running Android 4.0 or earlier, it's clear the future lies in HTML5.
"Devices that don’t have the Flash Player provided by the manufacturer typically are uncertified, meaning the manufacturer has not completed the certification testing requirements. In many cases users of uncertified devices have been able to download the Flash Player from the Google Play Store, and in most cases it worked. However, with Android 4.1 this is no longer going to be the case, as we have not continued developing and testing Flash Player for this new version of Android and its available browser options. There will be no certified implementations of Flash Player for Android 4.1," Adobe confirmed in a blog post.
If Flash Player already exists on a device prior to upgrading to Android 4.1, Adobe recommends uninstalling it after jumping to Jelly Bean. Otherwise, you can expect "unpredictable behavior," Adobe said.
This isn't as sudden as it might seem. In reality, Adobe waved the white flag with Flash on mobile devices some time ago, announcing in November 2011 that it "will no longer continue to develop Flash Player in the browser to work with new mobile device configurations," choosing instead to "increase investment in HTML5."