Cleaning with the "pastes"
One note for new shooters who are looking at cleaning with the so called "pastes". First off, the abrasives are very soft, chalk type materials. These are not the harder, metal removal, materials like aluminum oxide or the harder and embedding silicon carbides. (Silicon carbide is hard enough to actually embed in most steels. You may know this type abrasive better as Clover Brand valve lapping compound).
The cleaning regimen of a match quality barrel is more of an art than a science. The cleaning steps are much dependent on factors such as powder type and loading of that powder type. eg V133 low pressure loads will build up faster than top of the window loads.
The pastes can be used two ways. The intermediate cleaning is done using a patch embedded with the paste. This is preceded by using a good solvent and brushing. It is followed by "washing" the residue out with more solvent wetted patches, followed by dry patches, and finally a lube agent to take away the dryness. Good lube agents can be thin gun oils, Kroil, NAPA Lock EEz, or Stan Buchtels colloidal graphite called Graphoil.
The second method of using pastes, and a much more aggressive process, is by using a nylon brush with some paste on the bristles and short-stroking as you scrub down the barrel. Again, precede and follow with solvent, patches and oil.
As to the products, the JB's have been around for some time. If they were harmful we would have already heard about it. Another great product is Iosso. It comes in a tube and contains a slight amount of copper remover in addition its abrasives. Iosso also makes nylon brushes designed just for the short-stroke cleaning mentioned above.