Some of those mother boards require the circ pump to be off at startup, and then when the signal closes the appropriate relay, there is a delay (new circ pumps are slow-start) and then the board 'expects' the flow switch to close.
If you are lucky enough to have an older mother board, or even if it's new but has the old programming, you can hot-wire the circ pump so it runs whenever the power is hot to the tub. Keep in mind this is 220 volts, and you better have the circuit breaker off while working on it.
Turn on the power, listen and look to verify the circ pump is running, then check for codes. If it throws a FL1 code, you are outa luck: it "wants" the circ pump off at start, until it tells it to run.
Something I have wanted to try but have not yet - connect the circ pump to the connectors for ozone. I think that the ozone relay opens and closes right along with the circ pump, and it's the same size and type of relay, so it should handle the current just fine. You'll have to swap the leads, turn it on and see. The worst is it may, again, throw a code.
HTH