For many years I've been preaching "don't do separate tickets" because if the inbound is late and you miss your "connection" you are on your own.
But then somebody here pointed me at the BA page about baggage
British Airways - Checked baggage where it says
Checking in baggage for connecting flights
Baggage will normally be checked to your final destination, provided your journey is on the same ticket. However, if you hold separate tickets for the flights in your journey, British Airways will only through check your baggage to your final destination if the connecting flights are operated by British Airways or by another oneworld airline.
So last week I did it. Checked in online for my LHR GRU flight, turned up at T5, went to bag drop, explained I had a separate ticket for on carriage GRU SCL and the agent didn't bat an eyelid. Tagged the baggage to SCL via GRU *and* issued our GRU SCL boarding passes for the LAN flight.
What would have happened if things had gone wrong? They didn't so I don't know but with through check in like that I can't help feeling BA would be on a sticky wicket trying to wriggle out of their responsibiities.