I had the same problem on my '07 Road King Classic. The rust was very obvious because the stock exhaust is slash up. I have seen this problem for several years on almost every RKC I have seen, even on some new ones sitting at the dealer.
My fix was to paint the area with high heat barbecue flat black paint. Here are the steps I used:
1. Use a 3M scotchbrite pad to clean off as much of the rust as possible. It gets into the corners very easily.
2. Blow off all the reside.
3. Use a liquid chrome polish to get off as much of the rest of the rust as possible.
4. Take a cloth with prep-sol sovent and wipe the area clean to remove any remaining chrome polish. Rubbing alcohol will do if you do not have prep sol.
5. Mask off the areas you do not want to paint.
6. Spray 4 or 5 LIGHT coats of barbecue flat black paint.
This made a huge difference in the appearance of my bike. The flat black paint looks just like exhaust carbon and I have no visible rust. I am careful to wipe out any water from the exhaust end whenever I wash the bike. I have had a little bit of rust showup after a few months, where the baffle is welded to the outer pipe, so I just repeated the process and it looks great again. It was much easier to do the second time because there was so little rust.