The Civil War started April 12, 1861. The Emancipation Proclamation was issued January 1, 1863. If the Civil War wasn't about slavery, then what the hell were they fighting over for nearly half the time of the war?
Second, if you were to show me an arbitrary person and tell me they were from the Confederacy, I could more likely than not correctly guess their opinion on race. So what if the designer shares in this opinion?
The only part of the argument I find persuasive is that states started flying it around the time of the civil rights movement. You offer no evidence that the correlation is causal; my only objection is that there was really no good reason to start flying it in the first place, regardless of time period. "Under God" was added to the Pledge of Allegiance around the same time, do you wish to imply that was also added in protest of civil rights?
As others have pointed out, Lincoln was a tyrant of the worst degree, imposing unconstitutional taxes, an income tax, deploying the military to enforce it, and jailing anyone who disagreed with him, without recognition of habeas corpus. I don't suppose you're trying to defend this!
There's every indication his position on slavery was 100% political: He needed the support of foreign powers and anti-war abolitionists; and there is still, today, active before the states, a Constitutional amendment that would permit slavery in individual states, approved as a measure to end the Civil War (North states signed on, but the South didn't bite, refuting both the notion the war was about slavery and the notion that Lincon was 100% principled on this issue).
Yes, both sides had absolutely despicable qualities, and even today, we do horrible things to foreign countries under the US flag. That doesn't make me ashamed of the flag!