To download the correct Adobe Flash Player installer for your system, go here:
http://get.adobe.com/flashplayer/
Make sure any optional offer check box on that page is unchecked, or you may get an installer with some other software bundled. It should be unchecked by default, but look to make sure.
Clicking the Install Now button on that page should result in being directed to a second page with a "progress bar." After a moment, a disk image file named something like "AdobeFlashPlayerInstaller_14_ltrosxd_aaa_aih.dmg" will be downloaded. The installer on that Disk Image will download and install Flash Player.
If you are unable to load that page, or get an error message instead of a disk image file, take a screenshot of the result and post it here. Make a screenshot by following the directions here:
http://support.apple.com/kb/HT5775
Be sure no sensitive personal information is displayed. To add that image to a post here, click the camera icon in the post editor toolbar.
It is possible, in this case, that you may have a compromised network.