sodium iodide does not prevent clumping. typical anti-caking agents in salt are: fumed silica, potassium ferrocyanide, alumosilcate salts [Na+ | Ca2+ | K+] and sometimes, more frequently in organic products: simple carbonate salts (also [Na+ | Ca2+ | K+]).

I know there are people who are afraid of anything with with the word “cyanide” anywhere in the description but ferrocyanides are really quite harmless. they are so harmless in fact that they are a common component of chemistry kits for little kids to make prussian blue.