I know there was an article in an old Baum Bugle called "Guns of Oz," but I haven't read it. In writing about guns in the Oz series, I'm probably going to mention many of the same things, however. The most famous gun in the series is probably the one the Soldier with Green Whiskers carries, which is never loaded. Well, hardly ever. He admits in The Land of Oz that he's forgotten where he hid the powder and shot to load it, and some later books have illustrations of his gun with flowers in the barrel. I believe the first time we see Omby Amby actually fire the weapon is in Ozoplaning, in which it's loaded with marbles. Scalawagons has it loaded with an even more bizarre substance, namely popcorn. In Ozma, he's armed with a spear rather than a gun, and appears to be much more proficient with it.
While the Soldier refers to his gun as the "only musket in the kingdom" in Lucky Bucky, this is obviously not true. In fact, muskets grow on a tree in Oogaboo, as do bullets.
At least, the text identifies the guns as muskets, but I thought those were single-shot weapons. When Jo Files encounters the Rak in Tik-Tok, he fires several bullets at once.
Admittedly, I don't know much about guns, and I don't know how much L. Frank Baum knew. The musket tree plays a significant role in David Hulan's apocryphal Glass Cat, in which the Bad Lads temporarily take control of the country by taking over the tree. And in Karyl Carlson and Eric Gjovaag's Queen Ann, Jo Padlocks' son shows a particular aptitude for firearms, therefore taking the name Jo Musket.
Other guns appear throughout the series, and since I'm working mostly from memory here, this list is likely not to be exhaustive. In Dorothy and the Wizard, the Wizard is armed with two revolvers, presumably from the United States. He also uses a pistol to fire a magical ball in Magic. In Emerald City, the Spoon Brigade of Utensia carries muskets that the spoons claim could kill Toto with one shot, but we never learn whether this is bluster or fact.
Corporal Waddle of Bear Center has a toy popgun in Lost Princess.
The Skeezer guards in Glinda are "armed with queer weapons that seemed about halfway between pistols and guns, but were like neither"; I'd like to know more about these weapons, but no more information is given. Notta Bit More's huntsman disguise in Cowardly Lion includes a fake gun. Grampa carries a gun throughout his journey, but I don't believe he actually uses it. In Purple Prince, Ozwoz's mechanical wooden soldiers are all armed with loaded guns.
The bandits in Ojo have guns, and Realbad uses one to shoot some birds.
Handy Mandy takes a gun, along with a bunch of other weapons, from one the Keretarian guards. She leaves them all behind when crossing the Munchkin River, but I can't help but think of the seven-armed girl in terms of role-playing video games. Holding weapons in both hands will often give a character multiple hits, so just imagine what weapons in seven hands would do. Wonder City has chocolate soldiers with chocolate guns, and Forbidden Fountain introduces us to Toby Bridlecull, a man whose two pistols are loaded with stinging Borderwasps.
I left out a few instances of firearms that I found of particular note. As you might expect, there are a lot of guns in Pirates. John Bell wrote a bit about this when Pirates was the Book of Current Focus on Nonestica. Not only is young Peter Brown depicted with various guns in the illustrations, but he also fires a cannon right into a castle boat.
One of the Crescent Moon's cannons is also employed in Captain Salt, albeit not by a child this time. When a lava baby ends up on the ship, Captain Salt shoots him back to his mother on Lavaland using the cannon. Speedy is also rather loaded with guns, particularly in the part dealing with the warring Roaraway Island. While they mostly use bows and arrows, they also have a cannon that fires a volley of arrows, and King Radj keeps a giant water gun that can sink an island. Speedy manages to destroy this secret weapon by using a ray gun that can melt metal.
As you may have noticed, there are quite a few guns in the books, but very few gun-related injuries. Pirates and Ojo both have birds being shot down, and the Rak in Tik-Tok is injured with three bullets, but most of the time the narrative gets around such things. Either the guns aren't used, or the characters are protected from them somehow. This strikes me as the authors being unwilling to show the ugly side of Oz and its surrounding nations. Where there are guns, there is almost certainly gun violence. Besides, guards would be unlikely to carry guns unless someone at least thought they would do some damage.
With Ozites being practically immortal, what would a shot that would normally be deadly do to them? We're told that, if someone is ripped to pieces, the pieces would remain alive. If an Ozite is shot, would they eventually heal from it, as the Rak claims he will? What if he or she is shot in the head? The question remains open. There's also the issue of hunting, which apparently takes place in Oz despite the fact that animals can talk. That aside, is an animal that's shot down not really dead? Will it start showing signs of life again if you wait long enough? I suppose skinning and cooking an animal would count as total destruction, but what if a hunter just leaves the wounded animal on the ground?