Adobe Flash Player for Chrome and 'Internet Explorer on Windows 8/8.1' is built-in, so it should be up to date assuming you 1. have an updated browser 2. you use Windows Update.
Firefox / Opera / Other browsers use the Flash Player plug-in which runs background service to check for updates.
I suggest you use Google chrome because Adobe Flash Player is directly integrated with Google Chrome and enabled by default and you only need to always update google chrome