Re: What's with all the Union Jacks in the trailer?
Why wouldn't Britain still exist? The land is still there and people live there. Once the Federation comes into being, it isn't like they renamed everything. The United States isn't Land Zone Gamma, it's the United States. Kirk says that he's from Iowa, showing that the individual states still exist and McCoy talked about Georgia a few times. If they still exist in some form, then other countries would as well. The Earth government probably has standard laws for the whole planet, but the individual countries probably work similarly to the EU or how the states in United States work. Basically each runs itself in a limited fashion with certain aspects left to the Earth government. They probably keep the flags as a symbolic or historic thing.
"Libertarianism is a good idea on paper, until you look at it."
-Greg Proops, The Smartest Man in the World