LAN Chile/Peru would accept any ICAO license if you meet all the requirements.
After been accepted, LAN will be in charge of the license issuance.
During the Indoctrination/Initial Ground School, the applicant would have to take an ATPL/IFR multiple choice test at the Chilean or Peruvian's Aviation Authority.
You are also gonna have to take during that period an ICAO English Level exam in those countries, they don't take into consideration your actual ICAO English lvl for the issuance of a license.
Don't worry for the paper work, everything is going to be done by LAN.
The ATPL/IFR multiple choice at the DGAC is the same LAN is going to take you during the selection process.
I think that you can down load the Questionare ATPL bank from the Chilean/Peruvian DGAC websites.
For the IFR test I would recommend you to buy an IFR test prep from ASA or Gleim, you can also buy those on line.