So I have my Steam and Xbox accounts linked, and am wondering if it's possible to buy AC through one platform, and have it appear on the other.

If you're doing this to get around region issues on steam, don't. Just submit a bug report on the support website.

I'm doing it because I want to take advantage of Microsoft Rewards points to get some free AC if possible.

You can log into the game through your MS account on MS Store PC or xbox, claim anything they'd gift you there, then go back to play on Steam. The AC will be added to your game account. It's perfectly legit as far as I know, since you are getting it from official sources.