Actually, the main result of the war was the near complete demolition of all infrastructure in the South, the razing of every major southern city, the wholescale death of a whole ton of southerners and the near complete annihilation of the economy and political rights of most southern states for about a century to come.
The right to slaveholding was indeed a major factor of the civil war, but equally important were the underlying economic reasons why the South wanted to keep slaves. Under increasingly dangerous tarriff regulation in Washington which favored the importation of foreign Cotton, southern crops were selling for considerably less than they should have been were Southern interests fairly represented at the Federal level. Coupling this with the expense of migrating off of a slave-based production system, is it really that surprising that the South chose to exercise an (arguably) Consitutional right to secession in the attempt of preventing the total economic collapse that followed reunification and forcible breakup of slavery?
Slaves or no, the confederate flag reminds me of a very serious failure of diplomacy on a national scale, leading to what was essentially an avoidable war with catastrophic results for some half of the nation's populace. Yes, only rednecks and white trash fly it, but I personally view it as a reminder of the notable omissions of most peoples' history educations in this nation.