I would suggest that after polishing your wheels, put a coat of wax (ie carnauba) on it (the same way that your would do so after polishing the paintwork of your car). Think of it as the clearcoat to your polishing job!!
Then try the most neutral cleaner that you can find to use to clean your chrome wheels. In this case, I recommend that you use the same car wash soap that you use to wash your car's paintwork.
What you do is that after washing your car, you should still have some car wash mixture left in your soap bucket. Instead of throwing it out, use it with the wash mitt that you use specifically for the wheels. Soap the wheels, then rinse. That should actually be enough to get the brake dust off the wheels!!!
In the past, I have use a wheel cleaner, which I found just does not do the job, there's no such thing as a 100% no-touch solution to cleaning your wheels. They are also very expensive, and may damage your wheels. I have used Simple Green too, which is very effective, but I believe that it also strips wax, which would negate waxing your wheels to begin with. So IMHO using car wash soap is the gentlest (and most neutral) means of cleaning the wheels!
You will notice the wheels get dirtier faster than the rest of the car. If I wash my
MCS once a week, I end up washing the wheels twice during the same week!!! But it's worth it, clean shiny wheels help make the car look cleaner even when it's not
