Just remember that the signal lines on a common ground pcb are high when not pressed, low when pressed. Using an SR flip flop like that, not so much a good idea because things can get wonky when both are high at the same time, which would anytime you werent pressing the buttons
Frankly, if I were doing it, I’d be using a single microcontroller chip, just because it’d be low number of components and close to the same cost, with way more possibilities. But that’s me. If you want to do it with just logic gates, that’s doable to.
You can do ‘press toggles on and off’ pretty easily, using whats called a T flip flop (T for ‘Toggle’). But, no one makes T flip flop chips. You’d have to use a JK or a D flip flop, tie the inputs high, and connect the button’s signal line to the Clock input for that gate. Connect the output Q gate to a resistor, and the other end of that resistor to the positive leg of the LED and the other leg to Ground and you’re good to go.
I’d probably start with (number of buttons/2) of these chips:
Connect your power to VCC, both NOT_CLR’s, both NOT_PRE. Connect your ground to GND. Connect the signal line for button 1 to 1CLK, the first LED positive leg to 1Q, the signal line for button 2 to 2CLK, and the second LED positive leg to 2Q. connect 1D to 1NOT_Q, and 2D to 2NOT_Q, viola on/off toggle on press.
EDIT: PLEASE NOTE there was an error in the original wiring description. The D’s should go to the same gates `Q lines, and NOT to VCC like I had originally described. My apologies for any confusion.