I think R' Hirsch's Horeb contains some philosophical development of kashrut, entirely in harmony with the Talmud. That might do it for her.
Another option is the Rambam's Laws of Forbidden Foods. (I believe it's available in English, too.) His writing and organization are incredibly clear. The only problems are that he isn't referencing the Talmudic discussions; and occasionally the Halacha today doesn't follow his practice (e.g. he requires meat to have chalita -- blanching in many cases after it's salted and soaked).
Which aspect of kashrut? While lots of it is in Chulin, there are other elements in other places. If you have one topic in mind, please ask again here.
For instance, there's the (non-Orthodox) joke in which God tells Moses "don't cook a lamb in its mother's milk", and (after several rounds of this) Moses says, "Oh God you mean I should have separate dishes, right?" "Fine Moses, do whatever the heck you want."
This happens because people don't know that the Written Torah explicitly talks about purging dishes from the food they absorbed food, but it's not with most other laws of kashrut. It's here and here instead. (Many of the discussions about absorptions and mixtures are actually in Pesachim, some of which also stem from Numbers 6:3.)
You'd have to do some serious homework and tackle one topic at a time with appropriate source sheets; also, some of these discussions are long and complicated, and can involve reconciling multiple separate Talmudic discussions. (See this, for instance.)
You'll also wind up covering opinions that are not followed today, some of which can get quite confusing!
The text I'd recommend is actually the Chochmat Adam. He's an incredibly good organizer and writer, following laws from verse to Talmud to present-day law. He describes studying his book as shopping at the mom-and-pop shop instead of a Mega-Mart: officially less selection, but they carry some quality stuff you won't find elsewhere; and you're in and out of there much faster and not feeling exhausted! I find it an easier, simpler read than the Aruch HaShulchan, but that's just me.
Here are the categories as I see them, very roughly:
- Which animals are kosher (fairly straightforward, you can find good English articles about the subject.)
- How to do kosher slaughter (the Torah says "slaughter as I commanded you"; Talmud tells us how)
- How to turn a kosher-slaughtered animal into kosher meat (check for organ damage; separate the forbidden parts; devein; soak, salt, rinse) -- this is also generally in Chulin.
- What is "meat and milk"?
- When dealing with a forbidden substance (or meat and milk, which are forbidden when mixed), what's called absorption? What about pots, mixtures, cooking together, etc. This is the big, complicated one.
- Rabbinic decrees -- bishul akum, stam yeinam, and the like. By nature, these will be Talmudic and not found in the Bible per se; the rabbis admitted as much.