In its opinion in Dariano v. Morgan Hill Unified School District, the Ninth Circuit rejected a claim by students that their constitutional rights were violated when school officials banned their American flag clothing during a Cinco de Mayo celebration. Affirming the district judge, the panel applied Tinker v. Des Moines Independent Community School District, 393 U.S. 503 (1969) to the First Amendment claims, distinguishing Tinker.
While school dress codes and their application can raise grave constitutional concerns, the context as the court explains it here seems to warrant the tailored of school officials, American flag or not.
More of my analysis of the opinion over at the Constitutional Law Professors here.
And lots more about school dress codes in Dressing Constitutionally.