^^ Whether the cogwheel had been used by the Nazis or the Communists (symbolizing industrial production or the industrial proletariat) or others is not the point.
Surely the designers knew how to google "cogwheel in flags" and you instantly see the countries or political organisations that used the cogwheel. If they didn't mind the possible allusions, so be it.
One question that remains unanswered: Why an archaic cogwheel in a flag from the 22nd Century? Are cogwheels an essential part of the warp drive systems in nuTrek?