I guess it depends on what the actual thing is and where it is. One of my American friends, who is about 17 or so now, didn't know the flag of Hawaii. There are differences between Connecticut and Wales, ones a state and one is a nation (and once a country in its own right).
Personally, I consider myself to be British rather than English. I couldn't care less what other nations think of the British/English. I'm secure enough in my national identity not to be concerned. It's amusing that some Americans are unsure about Wales - you've got something in common with the EU afterall!
The thing that makes me laugh is that in other countries/cultures, terms like Limey or Pomme would be seen as racist! I wouldn't be offended - who cares if the navy used to carry limes on board to prevent scurvy!
[anyone know where the term Pomme originates from?]