There are certainly real-life analogues. Pearls and ambergris, for example. I can't think of any official material about it off the top of my head, but your table, your rules!

There are two routes to go here:

Science route: kidney stones are largely made of calcium, oxalate, urate, cystine, xanthine, and phosphate in our world. Presuming dragon physiology is roughly the same as our world, there's nothing inherently special about these elements in game. Short of "reliquary" type of usages (think finger bone of a saint), there's no reason to think it is special. Considering dragon scale is used in armor, I have to assume any less exciting dragon "parts" would pale in comparison. Might have value as a trade good or interesting conversation piece to the right collector.

Fun route: this chunk of phosphorus can be used 1d8 times in place of normal phosphorus from your material components pouch, upping the damage die of any [fire] spell cast using it.

I would imagine them being chunks of sulfur, which could probably be used dyes, explosives, or fertilizer. So they could be quite valuable.

Sounds like a wonderful story arc. Looking for a buyer for a kidney stone while at the exact same time, infuriatingly, fending off assassins trying to steal the kidney stone. Which you would ABSOLUTELY SELL TO THEM if they would just reach out.

Do you advertise even more publicly, risking more assassins? Or do you stay more quiet, do research, try to figure out why people want this stone so badly and yet won't just buy the damn thing?

Make them a magical gem that does a small amout of elemental damage on contact like 1d4. The element should depend on the type of dragon/breath weapon they have. Ive heard they feel like acid or fire when coming out.

Anything from a dragon would be valuable, I’m sure even their pee is used to make an elixir of some kind. And even if there’s nothing inherently magical with a dragon’s kidney stone, there’s bound to be somebody that doesn’t know that that you could sell it to.

Depends on whom you're trying to sell to. The village trader? Probably not. The court's urologist? Per chance.

As far as other creatures, you would want to look for kidney stones from creatures in unique environments. In most earthly mammals, they're composed of (mostly) calcium. Look for things that have kidneys, but either don't have bones as such, or that have bones likely composed of something other than calcium. It would have to be a seriously magical creature, too; something so stuffed full of magic that it literally pees it.

The only thing I can think of off hand that fits all the criteria might be an Aboleth, and you can almost certainly get better components from them.

Have you considered the chance of bezoars or ambergris?

Stalking a dragon for the chance of the animal expelling such things would be a terrifying endeavour.

My insight on your question: if nothing else, some crazy fool would tout a dragon's kidney stone as an invaluable ingredient for alchemy or some obscure potion or the cure/treatment for some disease, just like rhino horn or pangolin scales or deer penis for chinese traditional medicine. So considering this possibility alone, even in our current reality a dragon kidney stone could be sought after.

Guess it kinda depends on what it's made of?

Even if as a material it's mundane, it could be worth something to the right buyer, as a natural curiosity?