Its called " Soap and Water"! Really.
I am not kidding you. Soap and water will clean out the residue of black powder just fine.
You may need to use a bore brush if you are shooting those Substitute Powders, and since they are smokeless powders.
You may have to use a modern gun solvent to dissolve some of the crud they produce.
If you shoot bare conicals, you will probably need to use a lead solvent, like Hoppe's #9, or Shooter's Choice, to remove the lead.
If you are using those plastic "shoes" around a bullet, then Shooter's Choice, or acetone, will remove the plastic from the bore.
But, if you are shooting a PRB in front of Black Powder, the bore will clean up just fine with plain old, Soap and water. I have used my liquid dish soap and tap water to clean my barrels for more than 30 years. I dampen a cleaning patch, or two( for a tighter fit) with water, then rub in some liquid detergent, and run the patch down the barrel while it sits in a bucket of water. I pump the rod up and down, to bring the water through the vent hole, or flash channel for the nipple, into the bore, and then push the dirty water back out of the barrel into the bucket. The bucket water is changed a couple of times, while I prepare another soap and water cleaning patch. I try to feel for crud using this technique, and will go to a bore brush if I have crud that does not seem to be dissolving in the water quickly enough. I also put a cleaning patch, damp, with soap on it, in front of my bore brush when cleaning my fowler( smoothbore). The bristles of the brush will work on a rifled barrel to get down into the corners of the grooves. In a smoothbore, they poke through the patch to hold it to the brush, and together they give the bore a good scrubbing.
While I own them, I have never had to use a bore scraper( breech plug face) to clean that plug face on any of my guns. The movement of the water in and out of the vent hole, and the water dissolving any caked on crud has always done the job for me.
Don't over complicate the cleaning part. No special cleaning formula needed, thank you. :idunno: :hatsoff: