Is it the American flag?
Is it a flag of a country that is being studied?
If both questions above are no, is there any relevance to the flag being put up in the classroom for educational purposes for that class i.e. a class that studies different areas of humanity?
If all of the above questions are answered no, it does not belong in the classroom. If one has no problem with it being in the classroom because the teacher is represented by that flag then one should not have a problem with a Christian teacher having a cross up or the 10 commandments up as those represent a Christian, or a teacher having a statue of Buddha on display if they're Buddhist.