The Constitution prohibits the government (i.e., a school) from prohibiting speech based on it's content. However, schools *are* allowed to prohibit any speech that interferes with the educational process. If other clubs are allowed to hang whatever "symbol" they wish, without censorship, and the GSA is prevented from doing so, request the school explain its decision in writing. Then contact a local chapter of the ACLU or another gay-rights group to see what they can do to help.
Whether or not the school is warranted in prohibiting the display of the Rainbow Flag depends on whether the school has a policy with specific standards as to what symbols might be displayed. If there is no such policy and the school decides on a case by case basis, the action might be considered arbitrary and an impermissible violation of students' rights to free expression. Matters such as you describe always are best handled in an non-adversarial manner. Before claiming any "right" to display the flag, it would be advisable to have a frank discussion with the school principal and/or school counselors. It might be that conditions could be agreed upon that are satisfactory to you and the school, and, if not, at least you would have a clearer idea of what reasons the school might advance to keep you from displaying the flag, if that is their decision. That information could be very useful if you seek organizational support or decide to consult a lawyer.
The general rule is that speech rights should not be impeded. In schools, this is generally the rule, so long as the club is a recognized school entity. Please refer to a recent case (April 2008) in Northwest Florida (US District court), whereby a school student at Ponce De Leon High School was permitted to display a T-Shirt advocating Gay Pride. The school district had no uniform policy nor any other regulatory scheme in place to restict such a display.