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.
Beginning August 15th we will use the configuration settings in the Google Play Store to limit continued access to Flash Player updates to only those devices that have Flash Player already installed. Devices that do not have Flash Player already installed are increasingly likely to be incompatible with Flash Player and will no longer be able to install it from the Google Play Store after August 15th.
The easiest way to ensure ongoing access to Flash Player on Android 4.0 or earlier devices is to use certified devices and ensure that the Flash Player is either pre-installed by the manufacturer or installed from Google Play Store before August 15th.
If a device is upgraded from Android 4.0 to Android 4.1, the current version of Flash Player may exhibit unpredictable behavior, as it is not certified for use with Android 4.1. Future updates to Flash Player will not work. We recommend uninstalling Flash Player on devices which have been upgraded to Android 4.1.
Source:
An Update on Flash Player and Android ? Adobe AIR and Adobe Flash Player Team Blog