Like Bill Curtis said in another forum, there isn't any way, really. Kerr rifles bear dates of 1861-1863 (I've seen a photo of one supposedly dated 1864, but the 4 looks like a 1 to me, and the barrel serial number is not late enough to be 1863), and the ones used in the WBTS were the same styles that were being bought in England by the Volunteers and other private marksmen for long-range matches. I have never seen or heard of a Kerr rifle with any sort of Confederate marking.
There is a Kerr rifle in the Battle Abbey museum in Richmond, VA, that was supposedly used by a CS sharpshooter - no further ID - dated 1863. There is another in a private collection said to have been used by a sharpshooter in the Army of Tennessee - I don't know the date on this one. There is an 1861-dated Kerr in the National Civil War Museum in Harrisburg, PA, that was supposedly captured by a soldier in the 69th Ohio Inf., then used by him until late 1862.
Most surviving Kerr rifles differ from each other in small ways - sights, engraving, markings, &c. There were "standard" styles that the London Armoury Co. Ltd. marketed, but most of these sorts of rifles were custom-ordered, with whatever goodies the purchaser preferred.