To check the updates in flash player , open system preferences click on flask player , a window appears select updates click on check now .The result should come ok .
In safari preferences > websites > under plugins allow websites to use this plugin with the settings below it should be always on and not off .
And in the bottom setting when visiting other websites choose as on using drop down arrow selection .
See these articles Adobe Flash Player updates available for macOS on November 1, 2016 - Apple Support
How to use Internet plug-ins in Safari for Mac - Apple Support
If two adobe icons are shown on the desktop , right click on them and click on eject , the icons will be removed from desktop but the adobe application will still be there in system preferences or click on finder - in applications .
