Why don't they setup https://ruffle.rs/ on their website? I've managed to rescue a website using it and seems to work pretty much with all modern browsers.
Will point that customer to ruffle. They are not terribly sophisticated, technically, as you can imagine. Nor do they seem willing to spend any money to fix the Flash problem. Nothing about the site needs Flash, it could be implemented in plain HTML+Javascript. They just don't want to pay anything to do that.