I'll need to get some log files from you to troubleshoot the 'application initialization error'. Please review the FAQ Where do I find the Flash Player installation log on Windows? and provide all files listed: FlashInstall.log, Adobe_ADM.log and Adobe_GDE.log, so that we can troubleshoot the issue.
As an alternative, you can try using the offline installer posted at the bottom of the Installation problems | Flash Player | Windows 7 and earlier page in the 'Still having problems' section, however, without the installation log files we can't troubleshoot why the initialization error is occurring.
I was not aware of the offline installer, which seems to have worked.
Thanks for confirming the offline installer worked. We'd appreciate it if you could provide the Adobe_ADM.log and Adobe_GDE.log files so that we can investigate this further. Thank you.