You can't do that, but you can extract potassium chloride from the charred remains of the potassium chlorate reaction. If you melted potassium chlorate in a test tube and dropped sugar or anything...
Assuming you just try to get a purer gold, solve the potassium gold chloride in pure water, and slowly add a diluted solution of potassium hydroxide (caustic potash). This makes the gold precipitate...
No, they are different, potassium chloride is what you get when you react potassium and chlorine, and potassuim iodide is what you get when you mix potassium and iodine