As others have said it's a build up of brake dust. As they don't look like they've ever had much attention it will take a combined attack to remove all that iron deposit. That said, it doesn't take that much build up of brake dust on black wheel barrels to look like that. I used to have similar wheels on my last car and it was amazing how much it showed and I was pretty anal about keeping them clean.
I know you've already used Dragon's Breath but you will need to give it at least another going over with that, possibly more. Then, as Neil (WoWo) suggests clay it to get any remaining stubborn iron deposits off. Again you may need to clay it a couple of times.
Then once they are free from deposits, it's a case of maintaining that with regular cleans and use of a decent wheel cleaner like ValetPro Bilberry Wheel Cleaner diluted 1:10 with water, and using the Dragon's Breath 2-3 times a year, and applying a decent wheel sealant on a regular basis. Applying a good wheel sealant if the biggest favour you can do yourself, once they are clean and free from brake dust. Look at something like Gtechniq C5 or Gyeon Q2 Rim Quartz sealant. Application of this type of sealant is a wheels off jobbie but once done, it will repel brake dust very well and the majority of it will just fly off when you get the hose or jet washer on them. Failing that any decent wheel sealant will help to protect them.
