After cleaning & drying, I run a large, dripping sloppy wet WD40 patch up and down several times, and a couple minutes later dry patch it out...then run a patch "heavily" coated with Natural Lube 1000 up and down a few times...and stand the rifle muzzle-down in the cabinet.
Before a hunt or range trip I run a dry patch down and back up, then wrap it around a .22cal brush to slide all the way down into the patent breech and ensure there's nothing there...pipe cleaner through the vent, an alcohol wipe on the flint, pan, and frizzen, and load up.
If you use actual oil, you might need something like alcohol, but WD40 is so thin there's apparently nothing left to worry about after using it as I mentioned