JA's novels depict genteel society where ladies and gentlemen converse, dance and dine together. Militias, laws and punishment however, were taken for granted by people of JA's time.
I do not condone flogging but am realistic Georgian era attitudes to punishment were different to the C21st.
In JA's England, punishments were highly visible. I'm unsure it was always possible to hide stocks or whipping posts in every village from such delicate females as Lydia or Kitty !
To clarify, I suggested the girls may've seen the flogging of the private; There would no barracks... I also said they may've heard of the incident from Uncle Phillips.
As to what constituted a flogging offence, desertion is a possibility, something to consider later.