There are two valves commonly used in a brine tank. One is the air check valve that shuts off when the brine has been sucked out. It keeps air from being sucked in. You need an air check valve. On my Autotrol controller, that is actually part of the controller, so I just have a tube. I had not heard that any Fleck valves have air check valves built into the controller, but it is possible I guess.
The other is a safety float valve. That keeps the brine tank from overflowing in the event of a valve malfunction that happens to keep the brine fill cycle going. It also would guard against a power failure during the brine fill, although since the well pump would go off too, there is a limit to how much water would be available in that case. I don't have a safety float valve either. This is in a basement, so the damage would be limited compared to a brine tank in some other space. I'm keeping an eye out for a cheap used brine tank that has one. But also, my softener may not last forever, so I would get a new brine tank with safety float valve with a new system.