Static quiz module with predefined answers
Overall this is already pretty well organized and compact.  There isn't a lot of duplication or obvious abstractions that can be made.  It would be helpful to see the HTML to see if there are any changes that would make the Javascript easier to write.
A couple of suggestions:

Wrap the entire code block in an IIFE to avoid cluttering global namespace
 (function ($, undefined) {
     // Your code here ...
 } (jQuery));


Use .width() instead of .css('width', ...)

Some of your variables are only being referenced once and can be inlined:
 $('.flag').on('click', ...); // etc.