You are probably going to laugh but I will explain my reasoning. I looked online and on youtube and here too. There are all sorts of suggestions on what to use ranging from Diet coke and Aluminum foil to miracle polish to 409 and a scrub brush.
I looked around at what I had and I was pretty sure that if a power washer and soap didn't remove it before they probably weren't going to do the job now. So I looked at what I had in the shop and in the house. I tried rubbing alcohol first, but that only removed a top thin glaze layer and not much else. The rim looked pretty much as before.
Then I though about the Coke idea. This isn't as crazy as it sounds at first as the phosphoric acid in coke reacts with rust to help remove it. Commercial chrome sprays such as Mother's have phosphoric acid, just in higher quantities. I got a bottle out of the fridge and dumped it on there. Waited and sprayed and...nothing.
I figured I would turn this into a real experiment of sorts so I started thinking of some common products I could try. I mean, the rims are basically ruined anyway if I cannot clean them right? I looked on the shelf and saw a can of Goop hand cleaner and thought why not? I rubbed some in and then used a nylon scrub brush and amazingly it started coming off. It really was caked in brake dust and not rust.
So this is Dodgey's secret redneck chrome rim cleaning miracle:
Wash off with soap and water and dry.
Feel free to crack all the jokes you want about this, It is so off the wall that I am laughing myself.