Warm to hot'ish soapy water. A bore brush a few times and then hot tap water to rinse away the soap residue.
I found I got some of the flash rust if I soaked things for long. So now it's WHAM, BAM, ZIPPITY DO-DAH and DONE! Soapy water, bore brush for three passes, more soapy water, bore brush 3 more passes, rinse with hot tap water, dry patch until patches come out dry. At that point I push a patch folded over the end of an eye jag to dry out the blind end of the chamber. Nipples get removed and cleans along with the offset block that takes the nipple. Or for my flinters a pipe cleaner through the touch hole. Once dry oil patch. The whole thing from start to oil patch takes 10 minutes or less.
I had the rust issue the next day like you did. But that was back when it was new. Not a problem any more. So it may have been the previous owner.
One thing I like to do with them is run the oil patch and don't run a dry patch. Then the day I take it out or the night before if I'm leaving early I'll run the dry patch into the bore to remove any gross excess of oil. The patches come out with the odd light stain now and then but mostly they are fine.
A trick a long time BP shooter mentioned to me for brass with Pyrodex is to have a peanut butter plastic jar with water vinegar and a dash of liquid laundry soap in it. Spent brass is put into the jar until you get home. This "brass soup" avoids a lot of the stains on the casings.
Almost forgot. The bore brush in a blind barrel. Normally you can't pull back the brush. That old Chinese finger puzzle thing...

But if you use a fixed SHOTGUN cleaning rod that has a "T" or good screwdriver like handle you can run the brush down then give the handle a twist to let the brush bristles bend to the side as you twist and pull. This trick is a little harder than normal on the brushes. But I still get a good lifespan out of them. If you can find nylon bristle brushes that would be even better.