Lots of good advice so far. For the barrel, any decent smokeless solvent will work from Hoppes No. 9 to the newer synthetics. I like the CLP Eezox.
For the breech flash hole, I
carefully use a torch tip cleaner after a long BH209 session.
One thing I learned, before you use any solvents, run a dry patch, both sides, down the barrel. This will remove 90% of the BH209 fouling, making the rest of your job easier. If your first patch down the barrel is soaked with solvent, you will need to do a lot more passes.
My routine is to
1. Run a dry patch
2. Remove the breech plug and toss it in a little jar with windex. The
vinegar formula works the best but I will use any thing out of a bottle I happen to have underneath the sink such as 409, Simple Green, Spic and Span, etc..
3. Get to work on the barrel and action - Pay attention to the breech area.
4. Last thing I do is work on the breech plug so it has had some time to soak. I will use a tooth brush, the aforementioned torch tip, a drill bit, even some very fine steel wool if some crud is not coming off.
5. Put it all together. Depending on long the gun will sit, I may leave the barrel a little wet with CLP.
That's it.