I'll need to get some installation log files from you to investigate further. Please review the FAQ Where do I find the Flash Player installation log on the Macintosh? and provide all 4 files listed (install.log, FlashPlayerInstallManager.log, Adobe_ADM.log, and Adobe_GDE.log). Upload the files to cloud.acrobat.com using the instructions How to share a document or a file sharing service of your choice. Post the link the the uploaded files in your reply.
Alternatively, you can use the offline installer posted at the bottom of the Installation problems | Flash Player | Mac page in the 'Still having problems' section. However, without the log files for the online installer we won't be able to troubleshoot the issue to resolve it.
I've got to head out now so I took the easy option with the offline installer. Everything seems fine now. If I have any further problems, I'll find the 4 listed files and send them over to you.
Thanks for the update. Much appreciated.