Future updates to Google Chrome will remove support for browser plug-ins entirely, and remove the bundled version of Flash Player.
In addition, Flash Player itself will stop loading content from the open web in a few days. You'll need to explicitly allow whatever content you need to use (see the Enterprise FAQ that Maria referenced above).
The enterprise enablement section of the Administrator's guide describes how to manage this:
https://www.adobe.com/devnet/flashplayer/articles/flash_player_admin_guide.html
Deploying the Flash Player config file (mms.cfg) is more complicated in Chrome than other browsers. If it was me, I'd be looking at using either the Firefox ESR, which will continue to have browser plug-in support for a few months, or probably Internet Explorer.
If you need to provide this service to a large number of internal clients, you might want to think about licensing and deploying a maintained version of Flash Player to your clients until you can migrate, or coming up with something more contained and secure, like an ephemeral Citrix host with a known-good OS and browser configuration that can be run on modern, patched clients.