Well, separate enough not to use national insignia and identifiers, not when it has its own comparable symbols available.
Similarly, it is rather seldom that one sees the words "United States" or the US flag on any USAF hardware, even though the nation is prominently present in two letters out of the four. And the USN doesn't paint Stars and Stripes on its submarine hulls, even though this would be a means of displaying the national symbol when the vessel is submerged or about to submerge, and would be far more impressive than the midget flags sometimes flying on the sails of the surfaced subs. Indeed, the USN is somewhat exotic in choosing to fly the national flag at all, rather than a dedicated naval ensign.
Starfleet is quite a close parallel to the USAF and USN in this respect, I'd think. Indeed, the "nation" of UFP is probably present in the letters "USS" already, these expanding to something like "UnitedFederationofPlanets Starfleet Starship". There's little need to carry the "national" flag in addition, and indeed no ship so far has displayed it; that many ships feature the text "United Federation of Planets" on their pennants is a nice gesture, but doesn't need to be carried over to all the spacecraft serving in that organization.
As for the circular UFP logo, it should be noted that this is not seen on the side of the dockyard building in the trailer. Instead, the Starfleet Command logo, with the prominent delta symbol rather than the starmap as the main motif in the center circle, is seen there.
Timo Saloniemi