This smells a lot like homework. So, first of all, go back to your textbook. Read about Mealy machines and JK flip-flops. You'll probably have been given examples of similar (if simpler) designs. Look at them closely and understand how they work. Don't skip this bit.
The thing that strikes me is the requirement to use JK flip-flops. Why these? What do they do that others don't? Well... they toggle, as well as clear and set. And what does this problem appear to need? Something that counts 1 bits, which can be cleared when a 0 is seen. Counting is basically toggling bits at different rates.
That's how I'd approach it. The state is a counter of how many consecutive 1s we've seen (what is the maximum number this counter needs to store, how many bits does that need, and what should it do when it reaches the maximum?). Then for each value of the input and previous state, work out what inputs each flip-flop needs for its next state (remember that there might be more than one - if this bit was 0 and needs to be 1, you can do that by either setting or toggling). Work out the logic to do this, add an output decoder, and you're done.