Starting March 1, AA has off-peak rates for Economy to South America. 20,000 miles (instead of 30,000) one-way. Business is always 50,000 one-way.
British Airways (Amex points transfer instantly) charges 20k/40k for Economy/Business year round. That's only for "one partner award", so you'll need to fly AA to Miami/Dallas-Fort Worth/JFK and then onto EZE. Alternatively, if you can leave from Miami, you can fly LAN.
BA doesn't charge an extra fuel surcharge for LAN flights and may not for AA flights if booked online (I'm not sure about AA, anyone with recent experience?)
If there are enough seats together on the same flight/s you will be able to use a mix of AA and Amex (transferred to BA) if needed.
But, as above, good to mention how many miles/points you have.