I've been monitoring flight prices for a trip this May to Lima in J. BA fly direct but are SO expensive and the schedule isn't great. 1) Considered LATAM - it's second cheapest to AeroMexico, but have heard many negative things about service and reliability - plus it has no lounge at the moment in Lima; whilst a minor issue, spoils a bit of the fun on a leisure trip - especially if delays are commonplace. The LATAM flights to Lima go via MAD or GRU - which is probably the same for the flights to SCL. 2) Considered Iberia (trying to keep to Oneworld for my Avios), but it seems to be just codesharing with LATAM so the same issues. 2) KLM/Air France seem to be doing some reasonable deals if you're willing to forgo Oneworld. They change at AMS or CDG out to South America. 3) Considered BA/AA out to Miami and from there down to South America. Keeps me Oneworld but is more pricey.

I'll be interested to see what you decide!