I thought I downloaded the DMG listed in the linked question but I downloaded from here:
Install the DMG located at this location and the installation works:
Is your user ID by chance a member of the wheel group? To find out, open Terminal, at the prompt type id then hit enter. The output will list your userID, what group(s) it's a member of and a number of other items. When you do this, do you see (wheel) in the output?
If it is, this is a known bug when Flash Player is installed using the online installer. We're working on fixing the bug, however, don't yet have an estimate when it will be released. In the interim, please use the offline installer posted at the bottom of the Installation problems | Flash Player | Mac page in the 'Still having problems' section.
uid=502(patrickseiter) gid=20(staff) groups=20(staff),0(wheel),12(everyone),61(localaccounts),79(_appserverusr),80(admin),81(_ appserveradm),98(_lpadmin),33(_appstore),100(_lpoperator),204(_developer),395(com.apple.ac cess_ftp),398(com.apple.access_screensharing),399(com.apple.access_ssh)
I used the other URL I provided to successfully install Flash Player.
Thanks for confirming. We hope to have this fixed soon.