How to connect input and output on Bistable Multivibrator
The LEDs should go in the collector circuits for each transistor, as shown above.  The 3.9K resistors should be reduced (470 Ω shown here) to provide sufficient drive for the LEDs.
Other than that, I would leave the rest of your circuit as is.
This circuit also has separate switches for the set and reset functions.
Other ways of triggering are as follows:

The circuit on the left uses a pushbutton, and connects up to the Trigger input of your original schematic.
The one on the right uses a SPDT switch; you could also use a On-Off-On center off switch.