Based on my limited experience anything less than 2,5 hours is quite risky as baggage handling can be very slow at SCL. The last time I was at SCL, I cleared immigration in 2-3 minutes and then had to wait for my bag with priority tag for 30 minutes (among the first ones to arrive) and then spend 10 minutes at waiting at customs.

Although LAN might have some policies for LAN passengers travelling on separate tickets, I doubt they apply if you miss your international flights as your tickets are issued by AA (technically they are under airport control but I doubt that LAN employees are willing to touch them if you miss your flight). AA has its own more flexible policies but rebookings done by AA requires award availability on LAN flights which is very difficult to find at last minute.