Be sure you turned off Adobe's updater. Go to Control Panel > Flash Player (32-bit) ... go to the Advanced Tab and select "Never check for updates (not recommended)"
Note: It usually downloads two versions (one right after the other) for me.
Open Alternative Flash. If Alternative is running then it has a little icon in the system tray (start it first if it isn't running). Dbl-click the icon & it should open a window and you can see a "downloading (xx%)" in the bottom left of that window. I would suggest you watch that and see if it is getting you multiple versions. As I said two is normal for me.
If current then it looks like this (notice the Done. in the lower left corner) ...
If your system does match the current version and it still keeps trying to download then let us know because then I would suspect there is another issue. BTW: are you logged on as an administrator?
**EDIT** Elmer: I do think it might have in the beginning but it hasn't since. My only guess would be that maybe it's similar to my AV, sometimes it has to update to one level just so it can turn around and update to yet another level.
I would say try rebooting and see if the problem continues, as I don't recall exactly when or why mine stopped.