Thank you for not clicking on the link in the email and posting a comment here first.
No, that is not genuine. We don't sent emails with links to update the Flash Player. Valid, genuine, Flash Player is only available from adobe.com, or from the 'update notification' dialog window (if you have elected to be notified of updates).
This page, http://www.adobe.com/security/prevent-phishing.html, contains information on phishing attempts and instructions on forwarding the email to our customer support team to investigate. The pertinent section is:
If you think you have been a victim of a phishing email purporting to be from Adobe, send a copy of the offending email to our customer support team so we can investigate.