The current version of Flash Player is 18.104.22.168
Flash Player is indeed embedded in Google Chrome and Google releases updates either via a full Chrome update or a component update. If you have Chrome configured to update automatically, you won't see these updates occur as they happen silently in the background.
If you use a different browser (IE, Firefox, Safari) you may get an update notification, but based on your description, you received a malicious notification and did the right thing by bailing out of the installation process. I would appreciate it if you would private message me the URL to these sites and I will forward them to the folks who handle this.
Also, since you keep getting this notification I recommend running a full virus scan, malware scan, etc on your system to ensure it's not infected with something that may be contributing to the behaviour.