I posted a response to your original query over on the Missouri board, and am also putting it here in the hopes it might strike a chord with some of the readers of this board. Bryce, I'd recommend contacting the Kansas State Historical Society in Topeka. They have online resources, but their search engine wouldn't necessarily pin down the memoir, if they have it. They have a very comprehensive index system on-site, albeit the old-fashioned card catalogue type.

In addition, I would go through the bibliographies of all the books on Jennison, and Jennison's Jayhawkers. Maybe the memoir show up in one of them.

Also, I wouldn't overlook name variations--Jack; Chiles, Child.... The NPS site is down as I am writing this, but wouldn't hurt to give the name variations a run through once it is back up again.

Since when you consulted it earlier it indicated he came out of the 15th Kansas Cavalry as a sergeant, it appears he may have served in a subseqent unit--perhaps one of the post-war cavalry units raised to deal with Indians (18th Kansas Cav., 19th Kansas Cav.). They were formed two and three years after the war, but followed the wartime numerical scheme. I have a major project going on right now with the 18th, and will look through my materials to see if anything pops up.

I can't identify Childs in a post-war census, but maybe his National Archives military and pension files will shed some light on a post-war residence. With it you might be able to locate materials in county historical society archives.