The "snowflakes" cant be "polished" per-se, like an aluminum or chrome plated wheel can. They can be "polished" like the car's paint.
They are a "machined" wheel, with clear-coat paint over the top.
clean them with a safe wheel cleaner(or soap and water). If the brake dust is 'cooked' into the clearcoat, try something like scrubbing bubbles spray. Dont use an abrasive brush, because again, they are covered with clear PAINT. Spray the 'foaming" scrubbing bubble on, and then get down there and clean by hand with a soft brush, or a rag. Dont let the cleaning agent soak for too long, or it can damage the clear coat.
I have used paint-safe "easy-off" oven cleaner on painted wheels that were "stained". quick spot-cleaning, then rinse thoroughly with water.
Once they are clean, and dry, you can use any automotive wax/polish to bring out a nice luster.
BTW, the wheel's worst enemy, is a neighborhood dog with a strong nose, and a weak bladder!