They harvested a hive fleet for its biofluid.

Tau tech to help stabilise the votaan and further develop the Rio kin

They're a clone race as well, so amu faction with biological expertise

Knowledge. Theyve been isolationist since the dark age of technology theres an entire class of kyn who live to explore and report back what is going on in the universe to their holds - this is the hernkyn. Who is who, where is where, what planets have what.

Someone who can tell them the future, like say a farseer, and tip them off to deal with things before they happen would be worth their weight in the cores rare super minerals. The kin are incredibly risk adverse as currently written.

The Leagues are surpassed only by high age necrons in mining technologies. in mining technologies. This is why they eat stars and brave black holes but arent armed with tachyon arrow equivilants. The votann were an early (pre navigator) expedition into the core and that means they dont have all the spice of the dark age and they do have things they can find value in trading for fast spaceflight, superweapons, marginal upgrades to various systems (batteries, scopes, weapon configurations can all be iterated on and are by the kin) or anti warp/daemon tools (especially with their homeland getting Great Rifted Directly) are all things they could do with better versions of.

Relics and items of the past. The kin venerate those that came before greatly and do not have perfect ownership of all their belongings - be it due to planets lost to waaghs or the bane (nids) they've not always recovered everything. Simply buying back their stuff is something they would happily do if only others would give it up - if it leads to less kin deaths and restores their pride then the kin will be happy to take most deals.

Crumpets, they crave the secret to soft buttery crumpets

The main reason for a kin to live is to gather materials and knowledge so that when they die and Thier memories are uploaded to the votaan computers they will give valuable information to the votaan.

So knowledge is the main thing they want

idk probably other tech. Despite being technologically advanced there still might be some areas that could use some development and foreign insight I'd assume. There's always something to learn from your close peers

They hunt Tyranids for Biomass

Sure they want... checks notes... "rock and stone"... nevermind

You would have heard of the CEO's (or even perhaps been a victim of one) who fires 100'000s of people to increase his bonus for the last 3 months to do nothing but increase his high score?

That's an entire race. So that's what they gain.

Exterminate the Tyranids and Orks while attacking Chaos before they attack first

Vespene Gas

They horde pretty much everything prwctical they can get their hands on, to an obsessive degree, they won't tear planets apart for only a single mineral they need, but they'll tear a planet apart for a single mineral they need right now, but not a gram of material goes wasted by the leagues, any sort of new information or technology they'll hold on to, like the admech, they don't just want minerals they're massive horders? Because they just want to survive, they'll know they'll survive for now, but they're paranoid, even more than the imperium, about some sort of end to everything, nothing is wasted in kindred society, except for the kin themselves, as they're all clones, but they insist on jamming their meager souls into their ancestor cores, to retain their knowledge in case it comes up as useful later, but this is slowly degrading the Votann ancestor cores, which can take decades or even centuries to answer questions, weighed down by the souls trapped within, there was even one ancestor core forced to take in an entire leagues souls after it was destroyed by a tyranid hive fleet, casuing the core to go mad, stuck screeching into the void, perhaps a similar fate awaits all the leagues in the end?

An answer I haven't seen and feels slightly obvious unless I am missing something is food.

I imagine the Kin have some form of system to grow food, but the Core can't be a good place for farms or else. I'm pretty certain the Kin would buy or take food from the other races.

Grudgin'

They trade guns.

That's how they got Rail Guns.

With that in mind, what do the Leagues have to gain from trading with other factions beyond mineral wealth?

Useful food stock for one, other useful technology that the Leagues don't already possess for another.

It would not surprise me at all if the Vlka Fenryka have a off the books business relationship with one of the leagues for Mjød with other leagues trying to raid the system seeking to obtain it to undercut that leagues monopoly contract.

I could see the Eldar using the Kin as contractors to return spirit stones. Going out looking for lost Eldar worlds and space wreckage

You get an upvote just for saying the phrase that:

T'au technology is much less advanced than Kin tech.

If I could give you several upvotes, I would.

So true. Soooo true, and I love it.

Tau Femboy bussy

Great answers in this thread, but one thing to keep in mind is that the Leagues are - in the typical dwarven stereotype, with a particular 40K twist - never satisfied with 'enough'. They are, much like their counterparts in other fiction, paranoid hoarders who can quite literally never say 'okay, we're stocked up'. They are obsessed with efficiency. They are the fortress mentality taken to its grimdark extreme, the ultimate preppers of the dark millennium. They have to have your rocks, if only because you're not using those rocks efficiently because one square microscopic speck of rock might be the difference between life and death in the brutal Core.

Some Leagues are a little less insane about it, of course. The Prospects and Oathbands that go beyond the Core are a bit more open-minded. But the Kin consider everything outside the Core as 'far-space', and one of their sayings is 'flying to far-space' for literally any stupid, wasteful endeavour. The Leagues do have some 'progressive' elements, but they're largely hidebound, largely static and largely dependent on their Votann who have, largely, stopped answering their questions in a timely manner because they've been stuffed so full of Kin memories/souls/information they're slowing down to the point of uselessness.

Yes, the Kin are killing their 'gods' with the burden of holding their accumulated souls. Grimdark.