I am not clear what it is you are asking, is it if the JK flip flop correct logic wise, or why is the simulator not working, or both.If you are using a logic simulator, which one is it? I assume if you are using one that the LEDs are simulated indicators.Looking at your circuit, which appears to be correct for a basic JK FF, you have to be aware from it that the J and K inputs have various states. Check the truth table and set up the J and K inputs according to it and see what happens.
This particular circuit has problems associated with a condition called "race", so an additional stage is used to change the state on an edge, rather than a logic level.Cheers,
Richard