They could not be honored under the current city, state, or federal flags. That is an impossibility that Lincoln would immediately have recognized. Ask any flack.
“The furthest thing from Abraham Lincoln’s mind,” Spence Jackson reportedly said, “would have been to interfere with the honoring of fallen Confederate soldiers by families, comrades or their ancestors.”
Feel free to use Lincoln for anything
The governor of Missouri (named "Blunt"!) sent forth his press secretary (named "Jackson"!) to declare that Abraham Lincoln would have favored the raising of a Confederate flag at a Missouri cemetery.