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.
You can also try the standalone installer posted at the bottom of the Installation problems | Flash Player | Mac page in the 'Still having problems' section. If you get an error with that installer, I'll need the install.log file and FlashPlayerInstallManager.log file to investigate the failure.