I don't see any evidence that Stuart was fighting John Brown in Kansas.
The army arrived after the Battle of Black Jack to restore order, but I don't see where it took sides or participated in the warfare.
1rst Regimental records. Stuart promoted in Dec. 1855, and they were employed keeping the peace, until Brown left in Oct/Nov. 1856, having lost a son and whole lot else.
Regiment had run-ins with Brown and others, as well as pro-slavery people throughout 1856. During 1856 is when Brown and the command had several contacts with Brown. This was how Stuart was able to ID Brown in 1859 at Harper’s Ferry.
By 1857, Brown is gone and the regiment is more engaged in suppression of the Cheyenne.