Adobe flash player failed to register seems to be a pretty common problem now a days. Error happens when registry keys do not have admin rights even when logged in from administrative account. Uninstalling old version of the flash player will not fix the problem.
To get it fixed follow the steps below.
1. Run cmd from administrative account
2. Enter the bellow line of code (copy/paste)
secedit /configure /cfg %windir%infdefltbase.inf /db defltbase.sdb /verbose
3. Press enter
4. Reinstall/Update flash player
If the above fails. Download and install SubInACL. Once installed download this file. Unpacked file place in the same directory you installed SubInACL default location is C:Program Files (x86)Windows Resource KitsTools and run it. After couple minutes script will close.
Reinstall/update flash. Everything should work now.