Some of my most memorable bucket list trips have been to South America: Easter Island, Machu Picchu, Uyuni Salt Flats, Iguazu Falls.
You can earn Avios and redeem flights with LATAM, but unfortunately you can't earn tier points with them (as far as I know)
Intra-South American flights can be expensive for foreigners, so some redemption flights is probably the way to go! (eg. LIM-CUZ for Machu Picchu, SCL-IPC for Easter Island etc)
Enjoy planning your trip and keep us updated!