I'm having the same issue, getting stuck at 95%. I tried doing as suggested, and went to the linked page and downloaded what I thought was the offline installer (Flash Player for Safari and Firefox - NPAPI) at the bottom of the page in the 'Still having problems' section, but no dice. It still gets stuck at 95%. But it didn't exactly say it was an offline installer. Am I just downloading the wrong thing?
Could you try rebooting your machine. At times rebooting your machine does resolve such problems. If you still face such issues please share the logs(Adobe_ADM.log, Adobe_GDE.log and FlashInstallManager.log) from the affected machine. To get the location of the logs you can go through Where do I find the Flash Player installation log on the Macintosh? page. Once you have the logs please upload them. To know how to upload the logs go throughHow to share a document and share the link of the log file here.
I branched your topic to a new discussion. If you're using the offline installer and it still hangs at 95% you're issue is probalby not the same as the OP of the topic you posted to. What OS X version is this on?
Please read through the FAQ Where do I find the Flash Player installation log on the Macintosh? and configure your system to capture the various requested log files. Run the installer again until it stops. Take a screenshot of the installer dialog window (see How do I attach a screenshot?). Upload the 4 log files (Adobe_ADM.log, Adobe_GDE.log, install.log, and FlashPlayerInstallManager.log) and the screenshot to cloud.acrobat.com/send using the instructions at How to share a document . Post the link to the uploaded files in your reply.