In 1869, my greatgrandmother was a member of a group of 21 families that moved from Starkville, Mississippi, to Burleson County, Texas, a distance of about 600 miles. A letter by one of the members of the group, dated 2 Dec 1869, said that they had arrived in "Caldwell town". "We was about 6 weeks on the road." This is an average of about 100 miles per week, or some 15 to 20 miles per day. Actual mileage would have depended on the weather and condition of the road, which in their case was not all good, with some heavy rains and cold and very muddy roads.
The trip you describe is about 200 miles. The way from San Augustine to Caldwell (county seat of Burleson County) was a well known road, El Camino Real, or the Old Spanish Road, established about 1715, although it may have been used much earlier. (On today's road maps, look for Highway 21, or OSR.) The trip should have taken about 10 days to 2 weeks, depending on the weather.