I've seen many people that have written about FMA Brotherhood being like the Nazis. and yes the Nazi's do appear in the movie "Full Metal Alchemist, Conqueror of Shamballa". There's more to it. Ok here's my information about the FMA Brotherhood being like the Nazis:
Extermination (Ishvalans): This is very similar to the jews extermination, but 1st of all, the Nazis just took jews into concentration camps, FMA also did where they did experiments on Ishvalans on the Philosopher's Stone. The Nazis never killed all the jews on the target, but they killed millions on concentration and death camps. They also did experiments on how to kill/torture them.
King Bradley as Adolf Hitler: They have similar features, the moustache, their pose (King Bradley has his hands in front, overlapping, Adolf has his hands behind, but overlapping). They also ordered execution for millions of people (Ishvalans and Jews). There's many more for me to find, but right now that's all I have.
Ishvalans as Jews: Both believe in God. They didn't revolt except for a small part of them. They were put into extermination, Jews survived, so did the Ishvalans, but with a smaller amount of people. This has many in common, There's more for me to find, but that's all I have right now.
Experiments: They both used human lives to find what they were looking for. The Nazis used human lives to find medical treatments. The Amestris military used it for the Philosopher's stone (Which can heal people and give people power, you alreay know). That's all I have for right now.
Clothing: The Nazis and the Amestris Military are dressed well. Their "Pants" go all the way down, not seeing the socks at all. Instead of having those mini lines that shows the awards, like the navy ones, they have medals.
The Government: They have the same government, having the Fueher. The Fueher was a German title of leader. It was based on hierarchy but associated in Germany government.
The country: The Nazis wanted a one whole country with the same of everything, Amestris had many culture diversity before, but not anymore, it's mostly people that came from Amestris, Xerxes, Ishval, and many other cultures were wiped out or almost. The Nazis wiped out people that weren't like them around the places that they were taking over.
I know I will find more things, but this is all I have, if you guys know more stuff, please comment. Thanks