Nice. I found and attached the article and well, you miscalculated the amount of Oxone needed. You need 2 molar equivalents of Oxone and Oxone has a molecular weight of ~630 g/mol. a-methylstyrene has a mol weight of 118 g/mol and so 1 kg is about 8,5 mol. This by two and then by the Oxone mol weight and we get a whopping 10.700 g lets say 11 kg. And thats the problem. Otherwise it would be better then sliced bread as I can buy the styrene for less the 10 € per liter. Damn!
Nevertheless a great method and iodohydrin synthesis is something what comes handy in other places and very handy indeed.
And yes I calculated that correctly, I know of the nonsense that Oxone is sometimes said to have 314 g/mol but as half-molecules do not exist thats nonsense. It is 630 g/mol and it has 2 OXIDATIVE equivalents per mol. I attach another paper where you can see that at least 1,5 OXIDATIVE equ. are needed to get to the iodohydrin so with only two of those at all it cannot work.
Yields in the article were 81%, that would be 922 g, we usually do not get what those guys get, 800 g would be a realistic great result I would say.
Maybe this could be done with another oxidizer? Something less bulky. H2O2 should work, if somebody has access to concentrated H2SO4 and 30%+ H2O2 then Caros acid could be used and the volume greatly reduced. Just as a quick but sure shot.