I flew to Santiago a few year ago. Although on a slightly different routing. BA from Heathrow to Buenos Aires, with a stop for refuelling and change of crew at San Paulo Brazil. Then LAN from Buenos Aires to Santiago.
The LAN flight had a BA code share flight number. I was travelling on two separate tickets. One for Heathrow to Buenos Aires and another from Buenos Aires to Santiago. I was able to through check by baggage at Heathrow all the way through to Santiago. But at Buenos Aires I needed to collect my boarding card from LAN. I did not need to go landside to do this. LAN ground staff meet the BA flight arrival to assist connecting passengers.
I was very impressed with the LAN flight. Service was better than BA. Modern aircraft, and seats which reclined to near flat, but not as flat as BA Club World seat. More than adequate for 2.5 hours.
I received BA tier points and BA miles for the LAN flight. I can’t comment on Iberia as it’s a while since I have flown on them.