The proper way to store bits in JK flip flops
It's really hard to understand your question, but I'm going to guess that you mean that you have (up to) 16 different buttons, and you want the flip-flops to retain the binary value corresponding to the last button pressed.

The concept that you are missing is that of a "strobe" signal. This additional signal would be created by whatever circuit is producing the binary encodings for the buttons, and it indicates that at least one button is being pressed. Even if the encoding for one of the buttons is "0000", the strobe signal will be asserted, and can be used to update the flip-flops.

I'm not sure why you're presupposing the use of JK-type flip-flops. Normally, D-type flip-flops would be used in this sort of application.