In the instruction manual it says that if your city is in danger of being flipped the opponent's flag appears over your city. Does anyone know if your flag appears over an opponent's city if you're on pace to flip them?

Yes it does. :)

In the instruction manual it says that if your city is in danger of being flipped the opponent's flag appears over your city. Does anyone know if your flag appears over an opponent's city if you're on pace to flip them?

i think u just build a wall and u cant get fliped unless they make hollywood =P

Building a wall takes a lot of time, and costs as much as the early wonders. You're better off protecting yourself by making your own culture buildings like temples and cathedrals, or the culture based wonders. :)