I don't have a canon answer for you at all, but here's the closest I got from a preview thread.
Seven Samurai and Yojimbo are too embedded in my list of favorite movies of all time to NOT have at least a little bit about guns vs. samurai stuff going on in Tian Xia.
Won't be a lot if it does get in there... but it does have a good chance of getting in there somewhere.
Personally, I'd have them exist in Tian Xia but be very rare, having been invented several times, but brutally suppressed by the samurai each time. Maybe with the current political unrest, there's a chance for them to spread.
From my hazy memory, there is not much mention of firearms in both the Primer and the Gazetteer for Tian Xia (Which really sucks. Bring on the hardcover tome!)
Personally I think the following things would be happening:
-The Lingshen state military would be delighted with the technological breakthrough, and the chance to outfit thousands of state human soldiers with mass-produced AC-breaching power weaponry.
-The Samurai of the Black Daimyo and many Tengu (who adore the art of the sword) would have a vested interest in brutally suppressing the technology. Many samurai would also disapprove of the tech.
-The Tian Xia alchemists would invent an extremely volatile equivalent of a firecracker launcher, thus creating Golarion's first, highly temperamental, prototype bazooka.
|The Drunken Dragon|
Well...a couple things...
canonically, if James says there are, there are. He kinda made most of the world, and if its an idea he finds appealing its most likely in there. However, if they are in there, they'd still be pretty rare. I mean, the only reason firearms were even created on Golarion was because hey were necessary to survive an area where one of the most reliable forms of combat/technology/life had been made unreliable, inconsistent, or just downright non-existent (magic). As far as i know, Tian Xia has had no similar problems, so the idea of using fireworks and using the powder to use in weapons might not have occurred to them.
I also agree with Landon Winkler. If Tian Xia samurai are anything like Japanese samurai, they'd be pretty darn angry to have people using guns, since the entire idea was viewed as a little dishonorable and inferior, and so the ruling samurai would have made great effort to restrict the amount of firearm distributed or made. So even if they DID figure out how to make firearms independently of Dogun Hold's influence or due to it, I can't imagine its very widespread, and its probably frowned upon.
At the very least, I'd assume that guns might be found in Goka, due to traders passing through from the west.
Funny you should mention that. According to p. 17 of the Dragon Empires Gazetteer the first firearms made their way to Goka in 4620 AR only 7 months after they were first crafted in the Gunworks of Alkenstar, although the government of the independent city put heavy restrictions on their importation.