Battlestar Galactica (TV series) [1978]

Battlestar Galactica was a sci-fi show from the 1970-s featuring the escape of the last remnants of humankind in a fleet of spacecraft, pursued by machine enemies, the cylons. The human fleet is protected by Battlestar Galactica, hence the title.

The original didn't have the vertical flags the second Battlestar Galactica series had. Some flags were seen, though, used in the typical manner of "normal" interior flags.
Jorge Candeias, 12 October 2004 & 6 April 2006

A flag could be seen in the captain's office or quarters: plain beige with some brown logo within. The colour combination was similar to that of the fighter pilots' helmets (see this replica), except that the logo was darker and the background lighter.

The flag was folded, so I cannot say for certain what the logo looked like. The bottom part could match one or two of the triangles in Charles Self's flag of the Colonies, but the top portion of it doesn't match anything in that flag: There are no triangles there, just two narrow straight lines, similar to those found in the logo of the whole show.

Perhaps that's a flag containing the Galactica logo. It wouldn't make much sense in fictional terms - confusing a real-life graphical element (the logo of a TV show) with a fictional one (the symbol of a fictional spaceship, or of a fictional military corps - but it's possible.
Jorge Candeias, 12 & 15 October 2004

In an interview with one Charles "Chaz" Self, apparently a prominent member of the Battlestar Galactica fandom, flags are mentioned. (Scroll down until you find the question: BGR: You've also been working on some original flag designing for the Colonies...what inspired you to go in that direction?)

On Charles Self's site was a page with his flag designs. His first design, [for the Colonies as a whole], is relatively consistent with the flag on the show. The logo that appears in it, is the one used on the uniforms of fighter pilots as an arm insignia, more or less in that same colour combination.
Jorge Candeias, 12 & 15 October 2004