How to design new flip flop using JK flip flop
Build a state machine diagram.  Figure out the patterns by which one state goes to the next.  The inputs are the current state and any inputs, and the output is the next state.  Then add the JK excitation that brings you to the next state.  Make sure, at this point, that you have no duplicate states (i.e. states that with the same input that end up at all the same outputs) and eliminate them if you do. Once you have this, then start building Karnough maps for the outputs and JK excitations until you feel like you are ready to implement the resulting logic.