I am new Opera user, I just migrate from Chrome..
I facing the same problem, which adobe is not install correctly, and the plugin is not available..
I have google for solution , I even try manual installation, it does not work too.
finally, I managed to solve it by installing standalone flash player.
My Opera 25.0.1614.71
Windows 7 32bit
Goto page http://www.adobe.com/products/flashplayer/distribution3.html
Current version :
Flash Player 188.8.131.52 (Win and Mac)
choose : Plugin-based browsers
- Close Opera
- install the Standalone flash player,
- Open opera, now the Adobe flash is available.
The trick is "Standalone" flash player..
Other will not work for me..
Hope this help...