First Aircraft to appear in new LATAM colors will be a 767, two A319's and an A320

The first aircraft to fly in the LATAM color scheme will be a 767 from Rio de Janeiro Galeao (GIG) to Geneva (GVA) on a special flight on May 1 to retrieve the Olympic torch and fly it back to Brazil for the 2016 Summer Olympic Games to be held in that country in August.  The return flight will be to the Brazilian capital Brasilia (BSB) on May 3 where the Olympic torch relay will begin. 

This will be followed by regular commercial flights on May 5 from Sao Paulo Guarulhos (GRU) to Santiago (SCL) by a 767 and two A319's from Sao Paulo (unclear which airport) to Brasilia (BSB) and Santiago (SCL) to Lima (LIM).

The first LAN Argentina aircraft to appear in the new colors will be A320 LV-BRY (c/n 1351), which is currently being painted at COOPESA in San Jose, Costa Rica and is expected to be delivered in early May.

LATAM expects to have 50 aircraft repainted by the end of 2016 with the entire fleet appearing in the new colors by the end of 2018.  

Sources:

https://www.flightglobal.com/news/articles/pictures-latam-unveils-new-livery-424749/

http://linea-ala.blogspot.com.ar/2016/04/lan-se-viene-el-cambio-de-imagen.html