No, I don't believe your ancestor fought at Lexington in 1862. I looked up his online record on Missouri State Archives and see that he rode all the way from his home in Columbus, north-central Johnson County, in late December 1861 and early January 1862 to join Captain Duncan's Company E, 6th Missouri Infantry Regiment (CSA) where he was assigned 4 January 1862.
Those records are incomplete, especially for the southern side. It is my earnest belief that John W. Kinder served during 1861 in the southern Missouri State Guard, probably in the MSG 3rd Missouri Infantry, which had several Johnson County companies. This regiment was transferred with number and setup mostly intact into the Confederate army in early 1862.
No, I believe Kinder served in the MSG during the Lexington siege of September 1861 and perhaps in others of the MSG battles, too. Sadly, I cannot prove it.
Can anybody else prove Kinder's 1861 service in the Missouri State Guard?
Bruce Nichols