I may or not have got your question right.
I assume, as it's new, you're running Lion 10.7.4?
What I would do is go on to a site like CNET and download the Adobe Flash Player from there. If you are using Safari as your Browser, as soon as you Click "Download", a little icon will open up in the top right corner of Safari with a tiny download progress bar.
Many people arrange their downloads to be directed to their Downloads Folder, usually to the far right of the Dock. Assuming this is what you do by default, you can access the Adobe download either by clicking on the Downloads Folder on the Dock or by going to Finder/Downloads.
Click on the Adobe download. It will probably go automatically from a zip or dmg file to the Installer. When it opens, be sure to check the tiny box agreeing the terms & conditions and then the Install Bar will go from being greyed out to active and permit the installation.
I hope this helps and that I've understood your difficulty. As I said above, CNET is a well respected site for safe downloads. Of course there are many others.
Ian