Whoops, I'll fix that. It's Na2CO3.
The total reaction should be:
KClO3 + Na2CO3 K2CO3 + 2NaClO3
There are a number of problems, and you have to clarify what you mean, so we can help.
You have to balance the equation. That's a trivial point, but don't neglect it.
As was mentioned, all products and reactants are soluble. As such, there should be no precipitate, and also no reaction just by mixing in water.
I don't understand the electrolysis. You want a re-dox, and you may get one with electrolysis. You can get one with each reactant and product alone, or water alone (neutral salt for conductivity needed, but still). You can certainly get a reaction with lead strips during electrolysis, again, with each reactant and product alone or with plain water. So what are you trying to do?