There is no difference between any of the flags, except that there is a Supersonic Flag.
Excluding the Supersonic Flag, each flag provides a 10% bonus to your production and population maximum.
To start the game, you will be able to place a maximum of 10 flags (and one Supersonic Flag). The Embassy allows placement of 10 additional flags (total of 20). The Aerial Tower II allows placement of 5 additional flags (total of 25).
Flags are only available as gifts, which can be obtained from your friends, however sometimes Mr. Bill will send you a flag as a gift.