The question of "if the CSA had survived to the modern day, would it still have slavery legalized?" is an interesting one. The issue is that, basically, the reason that slavery was considered so indispensable to the South was that their farming systems required immense amounts of labor, and thus an immense labor pool that was cheap enough to still allow for profits. If you assume that agricultural development in this alternate universe followed the same course as it has in the real world, eventually the labor-intensiveness would abate, and slavery would no longer be an economic necessity. On the other hand, it not being necessary wouldn't mean it wouldn't remain in force...
The thing that really torques me about the Confederate flag -- and, to be honest, a whole lot of Southern-focused historical revisionism in this vein -- is that it's widely popularized by the lower classes, the same people who have suffered because of the South's massively ingrained economic inequality, and focuses so much on plantation glamour and the happy slave and other ways of romanticizing their own suffering. Yes, this is a natural human urge, but at the same time I want to take the whole thing by its metaphorical shoulders and shake it: "the 'Southern heritage' you're glorifying is that of inequality and oppression -- not just of African-Americans, but of poor whites! Of you, and your parents, and their parents, as far back as it goes! The plantations you fantasize about were built not just on the bonecrushing labor of the slaves, but on your ancestors' own spirit-destroying poverty! The 'states' rights' you wax poetic about were the rights of the states and their rich to grind your ancestors under their heel, and it was your ancestors' sons and brothers and fathers who died in droves for it! Don't glorify the plantation owners' cause -- they never gave a tin shit about yours!"
... I'll get my coat.