Here is what I believe is meant to happen. Anybody feel free to correct me if I am wrong.
Row 0 - When A is energized THEN Coil B is energized, but only for one scan cycle. That is what makes the flip flop work. (I am guessing that the P inside the coil means pulse)
Row 1 - When Z is energized AND B is de-energized THEN Coil Z is energized. This will be the row that keeps Coil Z energized.
Row 2 - When Z is de-energized AND B is energized THEN coil Z is energized. This is the row that energizes coil Z initially when you turn on A.
When coil Z is de-energized, pressing Button A energizes Coil B for one scan. This makes Row 2 true for one scan. This energizes Coil Z. Since Coil B is pulsed, even if Button A is being held down, Coil B is no longer energized. Since Coil Z is energized and Coil B is not energized, Row 1 is true and Coil Z remains energized.
Now release Button A and press it again, Coil B will once again be energized for one scan. This means that on this scan, Coil B is energized and Coil Z is energized. Looking at the conditions to energize Coil Z (Row 1 and Row 2) there is no condition that says "IF Z is energized AND B is energized" Coil Z will no longer remain energized. Once you release button A, the circuit is back in the place where we started.
In the photos that you have provided row 1 currently says; When Z is energized AND Z is de-energized, coil Z is energized. This is a problem because Z cannot be both energized and de-energized at the same time. What is likely happening when you try to run this is that Row 2 is true when you press button A (remember that this means Coil B is energized for one scan), Coil Z is only energizing for one scan cycle. On the next scan Coil Z is energized but Coil B is not. This means Row 2 is now false, and since the inputs in Row 1 can never evaluate to be true, Coil Z cannot be energized. This could be happening in microseconds, so you would never see it.
One way to see this in action would be to add a counter to your program that will count up every time Coil Z is energized. If you leave Row 1 the way it is, the counter should increment each time you press Button A. If you change -|/|- Z to -|/|- B, you should see the counter increment every other time you press Button A, meaning the flip flop is working as intended.