It consists of three islands: Robinson Cruzoe, Alejandro Selkirk, and Santa Clara. The only symbol of the Archipelago of Juan Fernandez that I know of is an emblem of the commune. Flag of Chile is the only flag of the islands. Chris Kretowicz, 11 April 2001
Apparently the Juan Fernández commune adopted a new flag as of November 2015 during their celebrations of the 441th year since the islands' discovery. The flag is divided into three stripes, blue, green and blue again. The blue stripes represent the ocean while the green stands for the archipelago's endemic forests. The stars represent the five islands that make up the commune (Robinson Crusoe, Santa Clara, Selkirk, San Ambrosio and San Felix) and each has eight points to point to the eight nationalities that comprised the original 20 families that settled the islands. The five lobsters represent the main source of employment on the islands and they surround a white sprig of a species of sandalwood that used to be endemic to the islands before it was wiped out.
The flag was adopted, to quote former regional director Daniel Paredes, to give the islands a symbol of their own so that they have something to represent them since they often feel secluded and ignored by the mainland government. This is extra obvious as the celebrations and the subsequent adoption of the flag were apparently completely ignored by the mainland authorities and thus I cannot say how it stands in relation to Chilean vexillological rules. Krystof Huk, 18 November 2016 Sources: http://www.vexilologie.cz/novarchiv.php and http://www.biobiochile.cl/noticias/2015/11/23/archipielago-juan-fernandez-celebra-aniversario-con-nueva-bandera.shtml