The Confederate Flag is not the one they are after. They are after the American Flag, the Stars and Stripes. But they know that they have to get the Confederate Flag first. From watching how they operate, if/when they get the Stars and Bars, the Stars and Stripes will be next. They will use the same argument[s] that they did against the Stars and Bars.
Thats really the thing about their argument, isn’t it?
They say they are for getting rid of the Confederate flag due to the CSA’s support for slavery. When someone with a bit of knowlege challenges them that it’s not the CSA flag but rather the Battle Flag of the Army of Northern Virginia, they shift their argument to how it was appropriated by the Klan and segregationists like Howell Heflin (Democrat Governor and Senator).
But they appropriated a lot of other things as well. The American flag, as you pointed out (look at be old early 20th Century pictures of Klan marche. You see US flags, not CSA or ANoV ones), the Christian Cross, etc.
There’s no reason to believe they’ll stop at the ANoV flag. So they need to be challenged about what is next for them.