Is flying the confederate flag a right?
Anything that's not illegal is a right. But keep in mind that you can easily tick off a lot of people by exercising some of your rights.
In the United States, the First Amendment to the Constitution guarantees citizens the right to freedom of expression. Flying the Confederate flag (or any flag, for that matter—even the Nazi flag) is one form of expression, and thus it is a protected right. Much of the controversy over flying the Confederate flag has centered around whether it is appropriate to fly the flag at public spaces like state capitol buildings, city halls, or courthouses. Since public buildings are not private citizens, they don't have the same rights and are subject to public scrutiny. The Confederate flag, from its very origins, has at least partly symbolized a movement that was designed to oppress and enslave African-American people. For this reason, many African-Americans, who have paid taxes to build and maintain these public spaces, take great offense when those public spaces then fly a flag that communicates such animosity and hatred toward African-American people.