In ST09 we actually can see three different versions of the UFP flag: Besides the "cogwheel" flag there's the "classical" blue one with the "United Federation of Planets" script at the shipyard and at the Academy exteriors and a white variant with classical logo and script also at the academy grounds.
Actually, I'll be happy if they got rid of the name at the bottom. Words on a flag are terrible
Now that I've looked at it for a while, the new "cogwhell" flag kinda looks like a telescope's eyepiece, with the stars seen through it. Kinda neat.