I recall re-reading that same paragraph on Kitty and Lydia's news of the regiment; the girls remark a private had been flogged, in passing.
Interesting shades of gossip on the Regiment; Officers dined with Uncle Phillips, discpline, a marriage hint.

My impression is anything to do with the militia could make for town gossip but more especially if it was social news. ;)
The Private seems just a passing remark by the girls.

*In a book called 'Mrs Hurst Dancing' ( G. Mingay. 1981) there is a watercolour by Diana Sperling, a lady who lived during JA's lifetime.
An 1816 illustration shows a genteel family watching a Review by the military.
I wonder if Lydia and Kitty saw the private being flogged or perhaps Uncle Phillips mentioned it to them.