You’re seeing lead streaks caused by the lead pellets being forced up and out of the wad as it hits the reducing/choke section.
Now the good news, don't be so quick to scrub the barrel back to a gleaming lead free finish. The lead streaks work in your favor to stop rotation of the wad as it moves down the bore. When after shooting cleaning, just run a lightly oiled mop down the bore to apply a protective coat and let it go at that for a few thousand rounds. If you have screw in reducing type chokes (read IC or tighter), then you may want to pull the chokes and clean them or the choke is going to produce a tighter pattern over time (read depends on if the choke is smoother bored or ribbed surfaces in regards to tighter/loser patterns and build up). When I do get around to really cleaning my skeet shotguns, I can push tubes of plastic (cased by the wads over thousands of rounds) out of each barrel/tube set.
Also, trash the brass brush, it just doing more damage than good. To remove the lead streaks, use a good lead solvent with nylon brushes.