I wrote this answer about Jews in the US and Austro-Hungarian armies in WWI, if you're interested! Overall, the US Army, in both WWI and WWII, didn't really make special provision for Jews who only ate kosher food, except insofar as they provided chaplaincy services, which often (but not always) included rabbis.

To focus specifically on WWII:

When it comes to Jewish law, it's not so much about a dispensation (in that someone has the power to absolve you from the sin of doing something, or gives permission to violate Jewish law) as it is about figuring out whether the law applies in a particular case. In no case, for example, is it ever permitted to keep kosher laws if it means that in the absence of kosher food one will injure one's health through starvation or illness. All of this meant that Jewish soldiers absolutely ate food while in the military that they would not have eaten if they'd have been in places where they had access to their choice of food.

What exactly this meant depended on one's level of religious observance, which definitely varied. For those who observed a strict level of kosher observance, even eating something as relatively benign as oatmeal or bread could be a problem, and so they were relying on the fact that they needed the food to keep up their strength as a justification. But even those who grew up with a less rigid set of kosher rules still, often, felt a sense of revulsion when they first sat down to a breakfast of ham and eggs or a lunch of pork. In one story I read, a soldier had just steeled himself up to eat the pork put in front of him when suddenly someone put a pat of butter on it, and that was what did it- he was too nauseated to eat it after that, at the thought of eating milk and meat together (another kosher law).

That said, as I alluded to earlier, it was often possible to get kosher food through the chaplains, such as kosher salami, matzah for Passover, etc. This food came not from the army itself but from the Jewish War Board, which I mention in the above linked answer. The packages sent by the JWB even included full "seder kits," with wine, matzah, kosher meat, gefilte fish and more so that army divisions could carry out Passover seders for their troops. In addition, many kosher-observant soldiers were mailed food by their families. Some soldiers were also lucky enough to be stationed in locations with kosher-observant Jewish families who might host them for the Sabbath and holidays.