I've actually been researching the influence of famous Nazi Walter Rauff's influence with the Chilean secret police DINA, so this is right up my alley.

The answer is no. There is nothing pointing towards any sort of influence from fugitive Nazis. The few that came to Chile were allowed to stay but they had zero connections with the government and usually kept to themselves and the occasional neo-nazi rally. Since Chile had and still have a large German community in the south, they felt right at home and many of the children to Nazi refugees still live there. Nazis who fled Nazi-Germany (and West/East Germany) to countries in which modern scholarship has proven influence from fugitive Nazis seemed to have a negligible impact on the country. I've written a post about the impact of fugitive Nazis in the Middle East which might be worth a look.

When it comes to the concentration camps, there is nothing pointing to any Nazi influence. Take the Chabauco camp as an example, in which the prisoners were incarcerated into an old abandoned mining town which was surrounded by barbed wire, watchtowers and anti-personnel mines. While the experience of the political prisoners were very much like those in Nazi-Germany or the Soviet Union, the widespread torture and abuses actually happened in a larger scale in the local detention centres scattered around the country. Memoriaviva, a Chilean human rights group that documents the human rights abuses carried out by the Pinochet regime, estimates the detention centres (including camps) at being over 1200.

Then there's the case of Colonia Dignidad. If you're Chilean, it will be hard to escape hearing about this concentration and torture camp run by a Nazi on TV, the radio or newspapers. But the truth is far more complicated than that. Colonia Dignidad was a village surrounded by walls, watchtowers and barbed wire and contained the members of a secretive Baptist cult led by a West German man by the name of Paul Schäfer. Schäfer, who was a Baptist preacher who fled from West Germany after being charged with sexual abuse against children, came to Chile with his family and set up this community. The story of Colonia Dignidad is both bizarre and tragic, being rampant with terrible story of isolation, sexual abuses, torture against members and child molestation. When the Pinochet dictatorship was established, the regime began to cooperate with Colonia Dignidad as a torture center where Mr. Schäfer himself was allegedly involved with the torture. Schäfer, who served in the German Luftwaffe during WWII as a medic, was quickly labeled a Nazi after the stories of the Colonia Dignidad was revealed and had to flee once more in the late 90's due to more allegations of child sex abuse, yet there's nothing that connects his past in the Luftwaffe to the SS or Nazi concentration camps. His methods were self-taught and had no origin in his time in the Luftwaffe.