You need an AR-15 chamber cleaning brush.
This has bronze bristles to clean the chamber, and steel bristles behind it that clean the bolt locking lugs.
You insert it in and out rapidly several times, then twist it half a dozen times... followed up with clean patches to take out any debris the brush has scraped loose.
You SHOULD be able to find the AR brush at any good gunshop.
I bought a mil brush, like the one Flyer described, at a gun show. I then bought a flexible cleaning rod that Hoppes sells. The two allow me to clean the bore with out removing the bolt assembly. Then brush the bore with a new 223 brush and your good.
I have a chamber brush and a Sinclair AR-15 Lug Recess Tool that I use on my Bushmaster. The challenge with the SU-16 is you cannot use a rigid rod and of course the Sinclair works only on AR-15 designs.
I tried the brush on the end of an Otis flexible pistol rod (ala Gun_Nut_2k1's recommendation) with success but it is a chore.