First, NEVER use regular firearm solvents in air rifles. Those solvents will damage seals used in air guns. Second, there are those that will say the same about brass brushes, but I've done it under extreme conditions. Remember, this is a low velocity rifle, powered by air, not gunpowder, you're not going to get the kind of leading and fouling you'd get with a firearm. Even with my high velocity PCP's I clean barrels maybe once a year, and I shoot quite a bit.
Typical procedure is to use a pull through rod like the Otis and a patch soaked in Goo Gone, that's a citrus cleaner available at any home center. If you can't use or don't have an Otis setup, week whacker line works just as well, cut one end at an angle, melt a blob on the other end, skewer the patch and slide it on down to the blob. Follow up with dry patches until clean.
Finally, your groups may not improve even after a good cleaning. The 880 is a BB/pellet rifle, and since .177 BB's and pellets are actually different sizes, the bore is a compromise that really doesn't shoot either all that well. Add in steel BB's beating up what is some pretty delicate rifling, and you have a recipe for poor accuracy. If you're looking for pin point accuracy, you're probably going to need to look at another rifle. Later.
Dave