If the kobold sits diagonally across from Kiri she will be just out of range; the carriage is not otherwise that large in any dimension. Kiri's sitting backward-facing, with one of the curtained windows between her and Aleko, presumably so she can read his mind if necessary.
The kobold sits just within range, but doesn't seem to have much to say, at least to begin with; she's too busy paying attention to the carriage ride itself.
The ride is pretty smooth, and if the kobold peeks out past the curtains it's pretty brisk too.
If Kiri doesn't have anything to say, the kobold will eventually scoot out of range and pass the time contemplating a bit of string in that casting-ish way she does.
Kiri has lots of things to say, but it's really hard to work with a limited shared vocabulary. Soechin she studied for years before she ever met someone whose Welchin was worse than her Soechin. She pulls out her vocabulary notes, sorts the words into categories, and then adds (marked differently) words she might want to try to add - hm, maybe she could overregularize and communicate the most common Welchin intensifier and softener and then use that for things like "sooner" and "less dangerous"...? (All this notetaking takes a while.)
The kobold will be over here contemplating her string, then, unless and until Kiri tries to get her attention.
...The kobold would probably have thought it at some point if it were dangerous to interrupt string contemplation. "Learn?" Kiri asks.
Next: prepositions. Fire in hand, on hand, under hand, next to hand, around hand, etc.
The kobold readily picks up both the words and the concepts, and shares the equivalent Animalperson words when she knows them, which is most of the time but not always.
Okay, question words. ...Maybe "question". "Speak want know: question."
Which is also useful: "Ask thing: what. Ask person: who. Ask..." She consults her notes, doesn't actually have 'place' - "here, there: where. Ask what person think, want: why. Ask now, soon, day, night - when. Ask one, two, more, less: how much. Ask..." This one's hard. "...go magic, go horse? How go? Ask, how Kiri find kobold? Kiri find kobold mind." Does that make sense?
(This is still much easier, she thinks at one point, than trying to do the mental gymnastics to teach a language she's not herself fluent in to someone she barely knows, with relatively little experience teaching anyone anything. She should probably work out a better way of handling the issue than leaving it to the other person, for future adventures, if she's going to possibly end up interacting with outsiders (which she wasn't expecting to) - but she'll think about that later. For now, focus on the task at hand.)
Kiri snorts and translates 'place' and 'reason'. More Welchin it is. She probably has a fair fraction of the animalperson words the kobold knows in the first place; it's either not a very complete language or the kobold hasn't heard that much of it, because her memory is really impressive. She reads off a random smattering of words in both animalperson and Welchin, identifies them all as "words", and then distinguishes between the "Welchin words" and "animalperson words" and declares both Welchin and animalperson "languages". Hmmm. Colors. She can do a surprising number of colors with fire, but most of them are uncomfortably warm for most people to be in close quarters with. Her outfit supplies examples of red and orange and white, her shoes are black, her hair is brown... "spring is green"... water is blue, she has a little gold on her person and it is yellow, and... purple will just have to wait, she supposes.
She shares the animalperson terms for 'word' and 'language' and the various colors, including purple, and also 'bright' and 'dark'.
Hmm.
"People want colors and games but need food and water."
...She doesn't have "if". "If here learn kobold mind, if there, no learn kobold mind." Did that get across the concept...?
And with "if" she can do all kinds of things like:
"If person speak 'mine', person own thing. ...Unless they're lying, um, 'lie' is, speak 'sun dark! Winter hot!'. Person speak 'mine' no lying, person own thing."
This elicits some mental grumbling about how ownership itself is a lie - she accepts this weird cultural thing, but only as a cultural thing, and she doesn't really approve of it - but also the animalperson word for 'lie'; apparently she doesn't know the word for 'own'.
"If person want thing other person own, person trade - one person own one thing, other person own other thing, trade, one person own other thing other person own one thing."
Trade, she's familiar with - apparently she trades with the tigerpeople, sometimes, though her thoughts about the memory she shares about that suggest that the trade itself isn't really the point there, and that there's something more complicated going on. Once she's established that she's got the right idea, though, she shares the word for that, too.
"If one person have... horse, other person have food, horse person no want food - food person trade money. Money does numbers - one two three four five - trade money any thing." She hasn't established "any"... "Fire be any color -" She cycles through some of the cooler options with a palmful of flames. Does that suffice?
'Any', she picks up with no problem - and here is the animalperson word for that, and 'some' and 'all' - but the concept of money seems to be completely new, and the kobold spends a little while thinking about possible implications of that (the one she's surest of: trade must be really important to humans) before she's ready to continue.
Kiri waits while she thinks it through - it's really interesting watching the entire concept of currency be novel to somebody.