It’s not even that, really . . . unless someone explains otherwise (meaning that I may be incorrect but I don’t think I am), servicemembers do not take an oath to defend the flag. Literally, they take an oath to defend the Constitution. Using “U.S. flag” as a symbol for “U.S. Constitution” (literally) opens a whole in the argument that someone like Scalia can pilot a freighter through.
Here' what I found:
"I, _____, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God." (Title 10, US Code; Act of 5 May 1960 replacing the wording first adopted in 1789, with amendment effective 5 October 1962).
I thought that the term was "lawful orders", but the meaning is clear.
I think we can all agree that there is no "flag burning" language in the Constitution.