The Fullmetal Alchemist anime universe places our own history and that of the FMA world on either side of the Gate that, Hohenheim tells us, exists in every human heart and spirit. Our history has produced mechanical science as its primary tool for technological advancement; the FMA history produced alchemy to the same ends. A great many things within the story follow this pattern—parallel but different.
Let us start with religion. In Episodes Forty-four and Forty-five, Dante tells us that Christianity is a dead religion, yet she is personally familiar with it and even names the Homunculi after the Seven Deadly Sins. Since she also tells us she is about four hundred years old, this gives us a timeframe for that death. She cites the Plague and witch hunts during her early life, which suggests that major events from our history occurred in hers as well, supposing that FMA history and our history are running at the same rate of time (1). Within that timeframe the most likely point at which Christianity might have failed is the early 1500s—the Reformation. In our history, this time resulted in an explosion of Christian sects as the Catholic church speciated into the myriad Protestant sects. The subsequent loss of the Church as a primary centralizing force resulted in the serious decline of the religio-political entity known as the Holy Roman Empire.
During and after the Reformation the Empire's constituent countries and kingdoms broke down into fairly constant war for a good two and a half centuries. Tiny kingdoms formed and reformed, allied and broke apart, and were traded about like poker chips in the game of diplomacy. If this also occurred in the FMA history, possibly exacerbated by the absolute failure of Christianity as opposed to sectarian strife, it could have been what shaped Dante's modus operandi. Despair and death, her favored motivation and means for creating the Philosopher's Stone, would certainly have been in plentiful supply during this period.
Amestris at the time of the anime, however, is enjoying the fruits of what appears to be a period of prosperity and, until recently, peace. This could fit well with the supposition that Amestris is equivalent to Germany, culturally and geographically. The Holy Roman Empire is known to German history as the First Reich, or First Empire. The Second Reich, a time of economic and cultural productivity, covers the period between 1871 and 1918 (WWI). Chronologically, this places the government that Bradley rides down in flames as the Second Reich; the general prosperity of Amestris suggests the same thing. The undesirability, from Dante's point of view, of such peace could explain why she went to the trouble of producing Bradley, a Homunculus that ages, to take over the country and provoke more wars. The transfer of power from executive to parliament, shown at the end of the anime, also parallels the forced resignation of the German Emperor at the end of WWI in favor of a parliamentary republican government.
This, however, is where things start to get a good deal more complicated, because the same could also be said of the Third Reich, also known as the Nazis, which held sway between 1933 and 1945. The aggressiveness of Amestris toward its own people, as well as its national neighbors, is somewhat more typical of the Third Reich than the Second. Dante's manipulation of the government from behind the scenes, by and for arcane ends, strongly echoes the occult mythos surrounding the Nazi government. It is clear that the anime writers are aware of this mythos and wish to draw upon it, as they introduce Hohenheim's involvement with the Thule Society once he enters our history (2). The Ishvarites, and the manner in which Amestris deals with them, also echoes, though it does not exactly mirror, the Jewish population of Germany during the Third Reich.
To expand on that particular point, the Ishvarite faith is not a direct parallel to Judaism, but some similarities do stand out. The most obvious is that they are monotheists within a generally polytheistic nation (ep 15). While the prevalence of Judaism's offshoots, Christianity and Islam, make it difficult recall these days, monotheism is one of that faith's original distinguishing traits (3). An argument can also be made for certain attitudinal similarities. The stoicism with which the Ishvarites bear up under persecution has also, at times, been characteristic of mainstream Judaism (eg Amos 3:2). The idea that the Great Art emerged from Ishvarite faith and philosophy to evolve into modern alchemy, as mentioned in Episode Thirty-six, parallels the frequent use of Judaic esoteric philosophy in our historical alchemical practice. The anime writers' use of an historically loaded image—undesirables being transported to designated camps by train—suggests that they drew these parallels deliberately.
Thus, it may be most accurate to regard Amestris as an alloy of the Second and Third Reichs. The historical imperatives that produced a military dictatorship, somewhat paralleling the Third, within the time period of the Second, are different from those of our history. The transfer of power to parliamentary government is not, in Amestris, associated with loss of a war, nor is it accompanied by the viciously punitive treaty terms leveled against Germany after WWI. This may mean that Amestris' new government will have a better chance for lasting stability than the Weimar Republic did. Certainly the FMA universe is not headed toward the Great Depression, at least not because of a widespread shift from wartime back to peacetime economy in the midst of massively short resources of everything. On the other hand, Amestris does have a large supply of soldiers who may be disgruntled by the reduction in military privilege and, perhaps, size, and a body of powerful Alchemists who may or may not now find themselves unemployed. It is possible these groups could produce the same kind of widespread unemployment and dissatisfaction that so helped the National Socialist Party in its bid for power.
Which is to say, while there are considerable parallel pieces between FMA history and ours, the pieces are not arranged in the same shape.