Brannon initially taught at a high school biology in Fort Wayne, Indiana.
He worked at the Marine Biological Laboratory at Woods Hole in Massachusetts in the summer.
He proposed and led expansion of the university's buildings housing science departments.
[2]: 19 He was also the university's director of athletics from 1896 to 1903 and head football coach from 1897 to 1903, compiling a record of 3–3.
He designed and gained approval for regulations related to milk that decreased the local incidence of tuberculosis.
He provided consultancy advice to a local company that prevented the growth of weevils in its breakfast cereals.
In the 1960s a new student residence building at University of North Dakota was named after Brannon.
[2]: 14 The library at University of North Dakota houses Brannon's papers and information related to his administrative roles.
[9] The University of Florida Herbarium holds 60 alagal specimens that Brannon collected.