|It might appear that nothing happened, but if you clicked Save, it is now in your default download location just the same.|
These days Adobe Flash downloads a manger first, usually to your default download location, it will have a red Flash icon. You then double click that which is the real downloader/installer and after it runs then it will open a page at Adobe where your system is tested for it's version. Look in My Documents for the installer or your own changed to download location. It will auto delete itself when run whether or not you get flash installed or not. If you don't want to download it again, save a copy to somewhere but never run it from there or it will do the same trick there too.
Last time I did it a week or two ago now, it failed to launch the test page correctly which fouls up the do nothing page that is perhaps confusing you. In the past the do nothing page suddenly came back to life and tested my version right away. This part seems to be broken for now so don't worry about this part too much. Just go to adobe and test your version manually.