I don't believe it was Jimmie Rodgers who precipitated a fight with the loud soldier during the early stages of The Red Badge of Courage. In Chapter I, the tall soldier (Jim Conklin) repeated a rumor he had heard about the regiment finally moving out. After he told his story, another private "loudly" disputed the tall soldier's story.

The tall soldier felt called upon to defend the truth of a rumor he himself had introduced. He and the loud one came near to fighting over it.

The loud soldier (Wilson) and the tall soldier argued again later in the chapter, but as in the earlier case, they never came to blows.

The only mention of Jimmie Rogers comes in Chapter XVIII, when after one of the skirmishes (in which Henry brazenly moves forward after the Confederates as they retreat), the men come across another member of the regiment who is going through his death throes. He had been severely wounded and was screaming and cursing at the men as they eyed him "thrashing about in the grass."

“Who is it? Who is it?”
“It's Jimmie Rogers. Jimmie Rogers.”