Most Countries in South America were Aligned with the US at the time and fought against the Axis in WW2. Did the Extreme right-wing dictardorships in South America have a Nazi/Fascist mentality hidden? For example Argentina, who was extremely antisemitic at the time, was one of the favorite destinations.
Argentina is something of a special case. Juan Peron, a military officer turned dictator, was a personal admirer of Mussolini, and had studied in Italy in the 1930's. Peron preached a nationalist, anti-capitalist, and above all, populist philosophy dubbed Peronism. The exact nature of Peronism is hard to nail down as it had support from both the left and the right, but it was very much modeled on corporatist and fascist ideals and rhetoric. Peron proved quite willing to harbor Nazi fugitives, both out of political sympathies and in the hope that an influx of officers, scientists, and other such personnel from one of the leading military and scientific powers of the world would help Argentina's development. Argentina also had a long history of German immigration. From the mid-1800's, the Argentine government had made great efforts to attract immigrants to settle the fertile Pampas agricultural region, and there were numerous Germans among these immigrants. As a result, there were strong German communities in Argentina at the time, and the generally awful state of Germany immediately after World War Two meant there was no shortage of new arrivals to blend in with.
Brazil also had a quasi-fascist government at the time, the "Estado Novo" (New State) of Getulio Vargas, modeled after the corporatist regime of Salazar in Portugal. However, Vargas also suppressed the even more radical right-wing Integralist movement, and declared war on Germany after a spate of U-Boat attacks on Brazilian ships turned opinion against the Axis, so Brazil's overall level of sympathy to fascism is debatable.
The escapes of many Nazis were also facilitated by that ancient bastion of Christian virtue in geopolitics, the Catholic Church. Church officials like Bishop Alois Hudal were some of the first to assist Nazis in escaping from internment, and it was clergy of the Argentine Catholic Church who made the first overtures towards bringing Nazis and collaborators to Argentina.
Altogether, South America provided the best chance at a new life for people who had committed atrocities against half of the planet. With North America, Western Europe, Africa and the Middle East largely under the rule of the Western Allies, the whole of Eastern Europe and Central Asia under the control of the Soviets who had paid so dearly for their victory, and Asia divided between European colonies and nations who had struggled against the militaristic nationalism of Japan, Nazis didn't have many places to go where they weren't reviled. Only in South America could Nazis find friendly governments and religious authorities, and large populations of German-speakers to hide amongst.