Each of the armed services has its own regulations for display of the US flag and foreign flags at its installations. Here is what the Army says in AR-840:
a. The flag of the United States will be displayed outdoors at all Army installations.
b. Only one flag of the United States will be flown at one time at any continental United States (CONUS) Army installation, except as authorized by the commanding generals of major Army commands . . . Installations which have other federal agencies as tenants may permit those federal agencies to display the U.S. flag on or in front of their facility.
c. The flag of the United States is the only flag that may be flown from a flagpole over a CONUS Army installation unless an exception is granted by TIOH, U.S. Army. However, the Minuteman flag . . . the . . .(POW/MIA) flag, the Retiree flag, or the Commander-in-Chief’s Installation Excellence Award flag, when authorized, may be flown beneath the flag of the United States without referral to TIOH for exception.
d. The flag of the United States should be displayed with foreign national flags at overseas installations according to applicable international agreements.
[TIOH = The Institute of Heraldry, the US Army authority on things like flags]
The Navy and the Marines follow NAVREGS 1260:
The national ensign shall be displayed . . . near the headquarters of every command ashore, or at the headquarters of the senior when the proximity of headquarters of two or more commands makes the display of separate ensigns inappropriate. When an outlying activity of the command is so located that its governmental character is not clearly indicated by the display of the national ensign as prescribed above, the national ensign shall also be displayed at the activity.
[Note that this applies only to commands ashore -- flag usage on ships is a whole different story.]
The Air Force follows AF Instruction 34-1201: Each Air Force installation is authorized to fly one installation flag . . . on a flagstaff placed in front of the installation headquarters. Additional flagstaffs and flags are authorized adjacent to each dependent school on the installation. Written requests for exceptions to policy are sent to the appropriate [Major Command] for approval.
So, in general, the regulations do say that there is only supposed to be one flag per installation or command. The catch is that it is *very* common for two or more commands to be located at the same base. For example, there are two flagpoles at the Washington Navy Yard where I frequently visit -- one by the ceremonial main gate and one by the waterfront.
The Navy and Air Force regs don't seem to explicitly address the question of foreign flags at overseas bases, but I'd assume that they follow the same practices as the Army.
Peter Ansoff