Nations, and allegiance to the state you live in, are still important. In some countries, the flag is not as important a symbol of the nation as other things (like a royal family, or cultural/religious heritage). But in the U.S., it is probably as strong a symbol as we have. This is not akin to arguments that references to Christ be taken away from school. You can choose to support or not to support any given religion in this country. But if you live here, then you are implicitly supporting the country and its core values/symbols. If you don't, you should not live here, IMO.
So yeah, banning the flag is a stupid idea. Teachers should be channeling kids' frustrations and differences in more constructive ways (debate club, sports, etc.). Not taking away the issue of contention when it is something that is a symbol of the very country you are living in.
However, this seems to be a silly question. As Shropt says, it is completely out of context and reads to me like those ridiculous questions Lou Dobbs used to pose on his website. Only a few wackos would seriously consider banning a U.S. flag from a U.S. school to reduce fighting.
*snicker* "Fair & Balanced" 
