Great pictures, thanks!
The silver box over the pump on the right is where you'll find your pressure switch. FL may just be a generic flow failure for your system. When the spa reaches temperature, your heater and pump cut off, but your pressure or flow switch may still be telling the system that there is water flow.
If you have a pressure switch, it should look something like
this. The knob at the top is adjustable. As you tighten it down, it takes more pressure to close the switch. Yours may be set so that the weight of the water alone is enough to close it. Or it may be shot altogether.
To calibrate it, attach an ohm meter or continuity tester with the pump on low. Tighten the adjustment screw until the circuit opens, then turn back a quarter turn so that it closes again.
You may also have a flow switch instead. In either case, take a look at the wiring diagram on the back of your control panel cover. It should label one of the small gray 2-wire cables as a flow or pressure switch connection. Then you can just follow the wire. If you have a flow switch, it will have to be pulled and checked for debris that might be holding it shut.