Share your experience!
Flash player is Adobe software.
It's NOT Sony's fault Adobe flash does't work on the Xperia Z.
Report the bug to Adobe BUT be warned they have stopped supporting Flash for Android.
Have you tried the latest version of Flash? Verision 11.1.115.81 is for Android 4 based phone's.
While it is true that the native software does not have Adobe flash, by which I mean Sony does not deliver the unit with Adobe, there are browsers available in the play store that will support flash. For instance, Dolphin Browser can support flash as of now. You can install it, and then download and install Adobe flash from Adobe flash archives for android 4, and you should be good to go. 2 things... 1) In the security settings, Install from unknown sources must be turned on for you to install adobe flash, and 2) In dolphin browser settings, you must enable Flash..
The problem is not of Sony's making..
Maybe this will solve your problem ?