My employment background includes almost 30 years in the hardwood industry. Everything from green lumber to kiln dried and then to finished product. Kiln dried lumber is first dried down to about 4% Moisture Content (aka MC). Then it is conditioned back up to 6-8% MC. It ain't gonna git any drier folks.
It can gain a little moisture though.
I've seen kiln dried wood (fire wood, cooking wood, etc ) advertised. I don't know what MC they try to dry it down to though. Just be aware that kiln dried lumber and wood are handled differently. Firewood sized sticks would probably "explode" if dried like lumber and turn into countless toothpicks.
Most well *air* dried lumber and wood (aka seasoned as we know it) is in the 15-20% range with a little of it down a bit further.
The problem with kiln dried lumber is that it is usually hard to catch on fire because it has no small splinters to light. Whiskers maybe, but few splinters. Whiskers aren't big enough to start the larger pieces. This is the reason for the billowing smoke. The second problem is once it is on fire the stuff burns very quickly and hot and wants lots of air. If you want to do a separate burn barrel and cook with coals it would work nicely.
The score at a lumber yard can be the off-fall from their green logs. I've seen off-fall from railroad tie length logs(8-9ft) to go from free to $10 a pickup truck load. Then you cut it to length and air dry it. If you don't stack it too tight it will dry quickly because of all the surface area. Yes it will have a bunch of bark but despite all the discussions, bark will burn nicely if there are thin edges to start or you can get the wood burning before the bark.
Sorry for being lengthy.