According to my copy of Uniforms of the Pacific War (Moller and Cerda, Partizan Press) most military flags were elaborate versions of the national flags.
The Murillo Squadron of the Bolivian Army in 1879 had a white flag with a burning heart of jesus in the middle of a wreath and Spanish quotes around it.Otherwise Bolivian flags were the national flag with the coat of arms in the middle.
Chilean flags are a bit diffrent
Battalion Navales (1881) had a blue flag with the Chilean Coat of Arms on it
Regiment Artilleria de Marina (1879) had a red flag with a golden star surrounded by writing in the middle and gloden anchors in the four corners.
Battalion No2 Aconcaqua had a blue flag with a silver star in the middle (1881)
1st Regiment of the Line Buin (1879) red flag with silver star in the middle
Battalion No1 Bulnes (1880)
Blue flag with red ciricle in the middle with the seal of the city of santiago
Battalion Czadores de Desierto (1879)
Chilean Flag with coat of arms of chule in the blue square.
Squadron Carabineros de Maipu (1880)
red standard with blue circle in middle with chilean coat of arms.
Peru
Peruvian national flags with coat of arms in middle. Symbols may change depending on unit.
So it seems on average
Bolivians and Peruvians=> national flags
Chile mix of national flags, and blue or red flags with a star in the middle.