I get repeated requests to update my version of Flash Player - I am running OS 10.10.5 on Google Chrome 51.0.2704.103 and Flash Player version 22.214.171.124. Google keeps telling me that they have the latest version installed and won't install any other version. I can't install on Safari as I keep getting the Google message when I do. I'm happy with what I have so stop sending the screen re updating.
Flash Player is embedded with Google Chrome and is updated with the browser updates. Adobe is not prompting the User for Chrome Flash Player updates. However, since you do not have the latest Flash Player version(126.96.36.199) I would recommend you to update your browser.