There's almost no evidence that the KGC actually existed in Missouri. There was an Order of American Knights that seemed to have some (but very little real) substance as a fifth column for the Confederacy behind Union lines.
The KGC was used as kind of generic description for guerilla groups early in the war and for fears of an alleged secret society among Copperheads behind the lines.
As a real organization, it had a marginal existence into 1862. But it never amounted to much outside of Texas and never to anything like the conspiracy buffs assert. Its founder and leader, George W. L. Bickley was captured going through Federal lines (under his own name and with KGC papers) in 1863 and the event had zero impact on the war.