Important editorial note: Vexillologists who provide this information and create these images are students of the science and art of flag design and history. Images of flags represented on FOTW pages do not necessarily reflect the politics or beliefs of the vexillologists who provided them.
Hispanic National Socialist Front (Frente Nacional-Socialista Hispano; FNSH) is a multi-national community of Hispanic-American Neo-Nazis, possibly only active online. While they use the old flag of National Socialist Movement of Chilean Workers as the common symbol, the national divisions have their own flags as well. In case of Chilean division, it is the old flag of the National Order Front - red-blue horizontal bicolor, charged with a white thunderbolt, shaped so at to resemble the letter N. Tomislav Todorović, 11 May 2016 Sources (WARNING: contain photos of people giving Roman salute):
[1] Presentation of FNSH: http://hispanons.weebly.com/acerca-de.html
[2] FNSH blog: http://hispanons.blogspot.com/
[3] Blog of FNSH - Chilean Division: http://hispanonschile.blogspot.com/
Movement of National Socialist Action of Chile (Movimiento de Acción Nacional Socialista de Chile; MANS) was founded in 1996 as the Horst Wessel Standard (Standarte Horst Wessel), and its present name was adopted in 2000 [1]. Its flag [1, 2] is red, with a large white disc, charged with an oak wreath surrounding a spade between two wheat-ears, all in black; these charges are borrowed from the flag used by the National Labour Service of the Third Reich but are differently shaped. Abbreviation MANS is inscribed in white in canton. While some images of the flag [1] suggest that these letters are oblique, the photo [2], when zoomed enough, reveals that they are not, even though the wrinkles make it difficult to decide easily. Tomislav Todorović, 11 May 2016 Sources:
[1] History of MANS and its predecessors: http://post-tenebraslux.blogspot.rs/2014/07/nacional-socialismo-en-chile.html
[2] Photo of the MANS flag: http://www.biobiochile.cl/2014/10/12/movimiento-nacional-socialista-de-concepcion-realizan-ofrenda-floral-en-el-marco-del-dia-de-la-raza.shtml
National Socialist Movement of Chile (Movimiento Nacional Socialista de Chile; MNS) was founded in 1932. Originally modelled after the German Nazi party, the party later distanced from the Nazism and eventually merged into the Popular Liberating Alliance (Alianza Popular Libertadora) in 1938. Its flag was derived from that of the Old Fatherland by addition of a red thunderbolt over all. Having been used by the oldest Chilean Nazi Group, it was reused in 21st century by the neo-Nazi groups such as the National Order Front. On the photos of the flag's modern use, blue and yellow look very pale and red looks rather dark, as if they were changed by age, but it cannot be decided whether this was really the case, or the new flags were made as such in order to simulate the age they don't really have. Tomislav Todorović, 10 May 2016 Sources:
[1] National Socialist Movement of Chile at Wikipedia: https://en.wikipedia.org/wiki/National_Socialist_Movement_of_Chile
[2] Photos of MNS flag from Valparaiso, on 5 September 2010 (WARNING: displayed people showing Roman salute): http://ciclodetransformacionprovidencialm.blogspot.rs/2010/09/alianzas-por-la-libertad-universal.html
National Socialist Youth (Juventud Nacional Socialista; JNS) was the youth wing of National Order Front. Their flag, which was displayed at the organization's website (no longer online), has had the same white thunderbolt symbol, but placed on a plain black field. Tomislav Todorović, 10 May 2016
New Fatherland Society (Patria Nueva Sociedad; PNS) was founded in 1999 at Puerto Montt. While describing itself as National Socialist, the movement insisted that the nation shall be defined by the culture, rather than the biology/genetics ("race"). In 2006, the Constitutional Court was requested to ban the PNS, which it eventually declined to do in 2010, after an unusually long procedure, stating that there is no sufficient evidence in favor on banning. Later same year, the movement dissolved itself, stating that it is impossible to safely operate as a legal National Socialist organization.
United National Socialist Movement of Chile (Movimiento Nacional Socialista Unificado de Chile; MNSU) was founded ("refounded", as they call it) in 1988. Its flag is derived from that of the original National Socialist Movement of Chile, with a differently stylized thunderbolt and addition of a red lauburu on blue field in the canton. According to them, the lauburu is a "Spanish solar symbol;" in reality, it is a specifically Basque symbol, but was obviously chosen here due to its resemblance with the swastika. Tomislav Todorović, 11 May 2016 Sources:
[1] MNSU blog: http://movimientonacionalsocialistadechile.blogspot.rs/2009/03/1988-el-comienzo.html
[2] Simbolos Patrios website - MNSU flag in the Chilean flags images gallery: http://simbolospatrios.cl/displayimage.php?album=44&pid=15897#top_display_media