"The American flag with the military oath of enlistment" is not "the American flag", but rather an attempt to make some kind of statement. At best it's political support of the military, at worst it's a possible dog whistle.
As in the oath that enlisted soliders/marines/sailors say: https://en.wikipedia.org/wiki/United_States_Armed_Forces_oat...
Anything else or other associations are in your head, not reality.
I'm not a US citizen nor I ever set foot in the US, and even from afar the quasi-fanarical displays of support for the US armed forces is a hallmark of supporters of the Republican party.
The left picked immigration so the right has to hate immigration, the right picked the military so the left has to hate the military. It's like our politics have to be polar opposites on everything, and it's exhausting.
This book had some great comments on military size and concomitant decline of power. https://en.wikipedia.org/wiki/The_Rise_and_Fall_of_the_Great...
The US military is not a partisan tool nor a domestic political estate, so that message is not overtly supportive of one candidate or the other.