Whenever people defend flying the confederate flag, they say it stands for "state rights". But what rights?

It might be hard for you to understand English, but the Tenth Amendment restates the Constitution's principle of federalism by providing that powers not granted to the national government nor prohibited to the states by the Constitution of the United States are reserved to the states or the people. If the Constitution doesn't disallow secession, the 10th amendment allows the states to make that choice.