Interesting that the Bible really doesn’t mention America’s position in the end times events. However it’s highly likey our military will be involved with so many bases throughout Europe and otherwise.
Joel 3, verse 2: "I will gather all nations and bring them down to the valley of Jehoshaphat. There I will enter into judgment with them there on behalf of My people and My inheritance, Israel, whom they have scattered among the nations; And they have divided up My land.
The Valley of Jehoshaphat is another name for the Valley of Har-Magedon (Armageddon).
So that tells me that all nations will be in the Valley of Megiddo, yet another name for Armageddon. But, it is the real name for that massive plain where even that great French general/dictator said it was the best place in the world for armies to fight. So, yes, in some form, the military of our Republic under our or other flag will be there. But, it will be an army of unbelievers. And, everyone there will die.