In the home dimension of Amber, normal gunpowder is inert, but you can use matches. Why is this possible?
The in universe explanation is that gunpowder (either black or smokeless, apparently, at least as known in the Shadow Earth) doesn't work; nothing is said about primers.
Military primers, well up into the era when the Amber novels were being published, used a chlorate mixture called "corrosive priming", which is almost identical to the mix in a safety match head, but civilian ammunition by that time almost universally used a lead styphnate based primer, which didn't leave corrosive residue, but didn't have the storage life of corrosive priming. If the matches used in Amber were also from Earth (very possible, as several of Corwin's siblings had apparently been visiting there, either "searching for him" or covertly keeping an eye on him), the primers in military ammunition would likely have worked, but in doing so with inert propellant, disabled the firearm (a "squib" load will lodge the bullet in the bore).
The matches Corwin used while imprisoned beneath Amber were book matches, which have the phosphosus separated from the match head and placed in the striking strip. The heads are a very good analog for corrosive primers, with the phoshorus acting as the igniter. This strongly implies that the propellant is the only inert component in Earth-origin ammunition. Corwin might have used the jeweler's rouge from Avalon for both from uncertainty; he'd been in the Shadow Earth since long before the invention of matches and might have been unaware they, and the chemically similar corrosive primers, would work there. He was, on the other hand, certain (due to prior experimentation) that the rouge would work for both.
Chemically speaking, black powder is similar enough to match head mix that it seems it should work in Amber -- but apparently it had been tried several times before Corwin's amnesia (or possibly that reference is to guns from other shadows than Earth). This implies that nitrogen chemistry (the only chemical commonality between black powder and smokeless, with nitrogen also being part of lead styphnate) doesn't work the same way there as it does here -- but chlorates seemingly do.
“Why is this part of the ocean, within the double of Amber, so different from waters elsewhere?” I asked. “Because that is the way it is,” said Deirdre, which irritated me.
I know its usually a trite answer but my take on the Amber universe 'logic' is that its working on a mystic level rather than physical.
ie. Guns don't work in amber because Amber's very nature was defined by Dworkin as like Arthurian legend. Swords and Sorcery.
The Forest of Arden is green and aboral eternally because it is the ideal forest, Rebma exists because reflections are real etc
When Corwin brings guns, they don't work because of the chemical properties of the jewelers rouge, but because Corwin's nature is a foxy tactician who comes up with clever solutions. He changes the nature of Amber. or rather brings forth this aspect of it.
We see the same sort of thing in the weirder shadows the characters travel to, or when they travel to shadows having the property of 'a brother will arrive to help me'. It's not the physics of the shadow they change or choose but the narrative of it.
You could argue that the only reason the shadow earth changes from plague london to the modern day is because Corwin is present in it and effects the change. All that time and Rein and Joplin are sitting around unchanged in Amber, not inventing new things or changing society.
For the same reasons most movies, tv shows, and games have their own set of rules,
Because, it's in the script
That is how cars explode with a cigarette thrown under them, bullets can curve in a complete circle, and many other events. Some things make no scientific sense but in science fiction it is exactly that, "Fiction" so they can do whatever the scripts and CGI, special effects, allow them to do