At some point, the Soviets had stolen various copies of American M2 Flamethrowers, which were previously used in the Invasion of Guam during World War II. They then started training some of their soldiers in the use of this weapon as well as researching it.
During Operation Snake Eater, after CIA agent Naked Snake managed to successfully bypass the heightened defenses of Krasnogorje and meet up with EVA, the flame troops were dispatched to locate Snake on Krasnogorje by Colonel Volgin. They were also ordered to prepare their flamethrowers to be fired at Snake if sighted, a job that was also considered a suicide mission as they would rupture their tanks if defeated, as Volgin wanted revenge on Snake for his kiling The Pain, The Fear, and The End.
Behind the scenes
The exact reasons for their presence in Krasnogorje, as stated by Sigint, will be different depending on the player's actions beforehand. If the player kills every enemy that they see, it will be implied that the flame troops came to burn Snake under their own volition in order to avenge their comrades. If the player either kills very few enemies or none up to that point, the stated reason will be that Volgin dispatched them to kill Snake as revenge for him killing The Pain, The Fear, and The End.
The gas masks worn by the flame troops are Russian PBF-models. These masks were made in late 1970s and were issued to Warsaw Pact soldiers, most notably to East German and Soviet paratroopers, riot police forces, and higher-ranked officers. Since Metal Gear Solid 3: Snake Eater is set in 1964, the use of this mask in Metal Gear Solid 3 is an anachronism.