National Socialist uniform

National Socialist uniforms were the uniforms originally worn by the military and paramilitary forces of Nazi Germany of 20th century Earth, during World War II. From 1933 to 1945, Adolf Hitler and the totalitarian National Socialist Party ruled Germany as the Third Reich, setting up a dictatorial system with unprecedented brutality and intolerance towards elements deemed socially inferior. The Nazi uniforms and symbology became synomous with this display of hatred, even centuries after their defeat in 1945.

The Nazi uniforms were re-introduced on the planet Ekos by historian John Gill in the 2260s in a vain effort to establish a more benign version of the Third Reich on that world. 

23rd century
In the mid-2260s, Earth historian John Gill established a new National Socialist Party on planet Ekos, in an effort to reproduce the economic revival of Germany after its defeat in World War I, but without the brutality of Hitler's regime. This plan failed when Deputy Führer Melakon took power. The Ekosian Nazi Party soon ruled the 'Fatherland' in a very similar fashion as had been seen in Earth's history.

National Socialist Party
Many officials of the Ekosian Nazi Party wore civilian workers uniforms without rank insignia. These uniforms were similar to the ones worn by the paramilitary security forces. In contrast to the original German Nazi practices, the Ekosian system allowed for women to attain high ranks in society. Several high-ranking officers of the party, in German called Reichsleiter (National Governors), wore military uniforms with Nazi Party rank insignia.

Army
The Army (German Heer) were the regular armed forces of the Third Reich, and also of the Ekosian 'Fatherland'. Wehrmacht units wore uniforms originally based on those worn by their predecessors in the Imperial German Army of World War One.

SS
Main article: SS uniforms and insignia

On Earth, the SS originated as a protection force for the security of Nazi Party officials, but grew into a fully-fledged army alongside the Wehrmacht. Three hundred years later, Ekosian SS units wore a variety of uniforms.

There were three colors of uniforms, two shades of grey and a black version. Officers usually wore caps with the totenkopf insignia of the SS, whereas soldiers often wore steel helmets.
 * Caps were not exclusive to officers though, as several guardsmen were seen wearing them.

SA
Originally, the German Sturmabteilung (Stormtroopers) was a paramilitary organization used as intimidatory muscle against political enemies, as well as "riot squads" used for political gang warfare against rival parties. On Ekos, SA members performed similar duties. Their uniforms were more civilian in nature, and were a light brown or khaki color.

Background
Most of the uniforms, including the ones worn by Spock and Kirk can be identified as belonging to the Leibstandarte Adolf Hitler, the first division of the SS. Although there are several minor hints of Adolf Hitler in "Patterns of Force", we are probably to assume he (or an equivalent) did not really exist on Ekos.

Almost none of the rank devices seen in the TOS episode match the spoken dialog. Furthermore, it is very likely that Kirk and Spock mistook Gestapo for SS, since Kirk readily identifies the totenkopf as identifying the Gestapo, which is unlikely since the Gestapo was not a regularly uniformed service. Furthermore, the description of 'Gestapo doctor' given to McCoy is nonsensical. These errors could be taken as ideosyncrasies of the Ekosian Nazis, ignorance on the part of the characters, or gaps in 23rd Century knowledge of the Second World War, but are more likely to stem from a lack of knowledge or a lack of communication between the costumers and the writers.

Deutsche Uniformen