Flag of Pucón, Chile. Gerald Clyde Abella, 21 December 2016
The figure in the center represents the Villarrica volcano, which is located a few kilometers from the city of Pucón, and those lines under it are the waves of Lake Villarrica. Villarrica volcano is the most active of all South America and its original name is "rukapillan" (the dwelling of the devil). Icho Urra Ponce, 21 December 2016
Unfortunately, no additional information was provided about the flag in the Facebook posts, including any sightings of the flag's use or official documentation of the flag's design. The design posted to FOTW's Facebook page shows a blue outline of a stylized mountain above two blue wavy lines, all centered on a white field. Stretching to both the hoist and the fly from the central design are five stripes of blue, green, yellow, orange, and red. Randy Young, 30 July 2020
One of the first confirmations that I have is that the flag of Pucón with the volcano and the lake and without the lines, is the logo of the municipality as can be seen on its website: https://municipalidadpucon.cl/.
A similar, but different, design for the flag of Pucón exists on Wikipedia (https://commons.wikimedia.org/wiki/File:Bandera_de_Pucón.svg). This design uses the same blue stylized mountain and wavy lines on white as the design posted on Facebook, but without the five rainbow stripes. The design was posted to Wikimedia by user Jlechuga86 on 31 March 2010, but there are no indications of the source of the design (e.g. if it was seen in public or derived from official documents). Randy Young, 30 July 2020