I have Windows 7 64 bit computers that are part of a domain and the various users use. They mostly use IE 11 or Chrome to use applications that require and updated version of Adobe Flash player. If I updated Flash Player by way of Adobe Flash Player Install for all versions on IE 11 using my domain account, is it installed for any user that logs on to the computer, or do they have to install it themselves as well?
It is installed for all the users on that machine. If Adobe Flash Player is installed by any one user, it is available for use for all users.
While you can certainly use the installer from Adobe Flash Player Install for all versions it is a shim installer that downloads and installs Flash Player silently in the background, as such an internet connection is required when using the shim installer. This installer is not meant for enterprise distribution, which appears to be what you want to do. Adobe offers non-shim installers for enterprise distribution via licensing Flash Player (free for most use cases) for enterprise distribution. More information is available at the following resources: