I presume this is from Surgeon James's journal, 1815, published in 1964 ?

The dark brown coats and trousers of the prussians are an enigma to me, unless he means a shade of colour that is described as dark gray elsewhere ...

But even "dark gray" could refer only to greatcoats, or to the gray jackets / stable jackets worn by the Prussian rank and file for minor duties. And these were more mid gray than dark.

The only brown Prussians I know of is a hussar regiment with brown dolmans and pelisses, and gray trousers.