I've tried this on 3 different OS X Machines, all running with Yosemite and Safari. I've downloaded the new Flash Player Installer, and attempt to install, but the installer gets stuck at the "downloading" phase, at either 25 or 30% downloading, and will not complete the download or the installation. I've never had this problem before. It seems that the installer / downloader is broken.
This morning we resolved a problem that prevented Flash Player installations from completing for some of our Macintosh users.
If you encountered this problem, please delete any previously downloaded Flash Player installer and either:
1.) Download the installer again from https://get.adobe.com/flashplayer
2.) Download the stand-alone installer from http://fpdownload.macromedia.com/pub/flashplayer/latest/help/install_flash_player_osx.dmg