Say we're talking about C major.
In C major the III is E major (a non-diatonic chord) which consists of the pitches: E G# B
If we do bIII, does that b mean I should flatten all the notes in the chord to: Eb G Bb. (?) Which would be an Eb major, the parallel minor's 3rd chord.
I've asked a new question for a better understanding of roman numerals.