I inadvertently uninstalled the edition of Flash Player that was on my Windows 10 suite. When attempting to reinstall, Adobe tells me the program is installed - but it isn't and doesn't any longer appear on my computer's list of installed programs.
I'm assuming you're referring to Flash Player for IE/Edge. Flash Player for IE/Edge is embedded in the browsers by Microsoft. The embedded version does not display in the list of installed programs, as it's considered a component of IE/Edge. Due to this, the associated files are locked and can only be deleted by brute force (e.g. modifying file permissions with some 3rd party software to unlock the files).
Due to Microsoft embedding Flash Player, the standalone installers will not run on Windows 10. You can try one of the following, but there is no guarantee that any of the options will work:
If none of these work and you want to get Flash Player for IE/Edge back you'll most likely need to re-install Windows. Contacting Microsoft for assistance is also a recommended option.
P.S. This is the same issue reported at I accidently deleted my flashplayer, but am unable to reinstall it from the site. How can I download it again? by someone else.