Hi Ian. I designed those flags, and in the course of my research I found an interesting post on an old user group that I will quote below:
“On my behalf, Bjo Trimble interviewed set designer William W. Thiess and we discovered that the United Space flag was three unequal stripes of cloth, dark blue, white, dark blue stapled together. These were draped and placed on the pole so as to simulate a draped horizontal tri-band flag. Attached to the top of the staff were two (one each) trapezoidal "streamers", one red and one white. Long time watchers of the show will recall that United Space was an early term for the
United Federation of Planets, perhaps even the fictional political entity which preceded the UFP. When that flags [sic] were reproduced for the 1972 Equicon (an Early Star Trek fan convention) in Los Angeles the white "stripe" was described as an "edge-on view of the Milky Way Galaxy.
Jim Ferrigan, 7 December 2002”