Since SCL-IPC is on the domestic side I assume you can't buy duty-free in SCL.

If you buy duty-free state-side, do you then have to check it for the SCL-IPC leg? If so, do you need to have a carry-on with you to put your duty free into and then check the "carry-on" or do you have to re-check your international bags (like entering the US) and one could add the duty-free to your previously checked luggage?

NOTE: All flights are on LAN.