Hi Michael, and welcome to FlyerTalk!
In general, I think most of us agree that it's best to centralize your miles/kilometers/points in one program unless you are a serious road warrior, and then you can chase status on multiple airlines. I live in SCL, but I mainly bank my flights with AA since I go to more places than LATAM flies, and also like the elite status with AA more than with LATAM (although you'll note I'm also LATAM Black, but I did that strictly for Oneworld airport services in the US on domestic flights).
When you make your booking, you can choose to register your AA (or any LATAM airline partner) frequent flyer number on your reservation, and then it should appear automatically on your boarding pass when you check in. You can see how you earn AA miles when flying with LATAM here:
https://www.aa.com/i18n/travel-info/...n-airlines.jsp. It can sometimes take LATAM flights a week or so to post to your AA account.
¡Buen viaje!