The mileage from Little Rock to a location during the war was usually given from the Ferry crossing. Within about a two block area of the ferry was the Anthony House it was headquarters to everything in Little Rock, M & LR Railroad, all the stage lines and the telegraph line. I have been a topographer for over 40 years. I used a map scale being 1/2"= 1 mile and plotted from the war time ferry location 25 miles along the old roads to the Camp Nelson site, (BTW I found the original Camp Nelson site back in 1982) give or take a 1/2 mile the 25 miles runs through the middle of Camp Nelson. I did the same thing for 28 miles and it runs through the middle of Austin, Arkansas. During the war there were three confederate camps near Austin, Arkansas, one West, one East and one South. All were referred to as Camp Hope/Nelson or Holmes at any given time, even though they were 2 to 3 miles apart. The South camp was Hope/Nelson camp. The Camp Holmes was the least used name especially after General "Granny" Holmes became more unpopular with the troops. Camp Hope and Camp Nelson are the same physical site, the first use of the Camp Nelson name, that I have found is dated October 14, 1862, this is about a week after General Allison Nelson death. The camp was renamed in his honor. Camp Holmes is a different site all together.
Now to answer your question on how they arrived at the mileage. A person or soldier of a 150+ years ago were akin to the land they knew miles traveled, with the help of locals along the road with good directions and an officer's map. Also land marks like streams, crossroads, big trees, homes and other topographical features gave them a guide for distance. When you walked or rode a horse everyday one knew miles traveled. In their letters or reports given, when they say something like "we marched twelve miles today and went into camp". They were right on the distance or maybe a half mile off. They might miss a compass direction slightly, but their mileage distance is usually spot on. On studying their distances given and putting it to paper, they have proven it to me.