Let's set the key to
When the given key uses a minor key signature you don't need to prefix a flat on the Roman numeral, it's assumed from the key signature. So, in
C: bVII the flat shows the chromatic lowering of the root from the major key signature, but in
Cm: VII the minor key signature already sets the flat on
Bb so you don't put the flat prefix on the Roman numeral.
Also, let's be sure to not confuse
Bb triad with
v6 (the minor dominant with
Bb in the bass.)
v6 is common with a descending bass, like
Cm: i v6 iv6 V.
If you are working with common practice harmony,
VII has a tendency to sound like the dominant of the relative major. In other words, the
Bb major chord to
Eb major, rather that sounding like
Cm: VII III sounds more like
Eb: V I.
On those flow charts, notice how
VII are both at the far left away from the primary tonal chords
IV. They are both out in the modal nether-regions and not very strong for defining the tonality. They are modal or secondary chords of a key. Functionally they are both pre-dominant. From them you would move along the flow charts to the left to get to the dominant function, and then the tonic function.
VII can also act like a alternate dominant with a modal flavor.
A common form that uses
VII is passamezzo antico where it appears both as a modal dominant and as the dominant of
A similar kind of harmony happens in Handel's sarabande in the suite HWV 437, but it also involves a harmonic sequence.
Dm: [ i V ] [ III VII ]
Harmonic sequence is another common way modal chords like
iii occur. In terms of function that can make them sort of ambiguous, because harmonic sequences are often used to change key.
...why would you have a i-VII-III... progression?
Don't treat those flow charts as a practical guide to harmony. Think of them more like very abstract representations of two basic music theory ideas: the fundamental tonal harmony progression is root movement by descending fifth, and functional harmony flows pre-dominant to dominant to tonic.
If you take the charts literally, then you can't even get something as fundamental as the Handel example
Dm: [ i V ] [ III VII ].
Keep in mind the flow charts makes no reference to phrases or barlines.
i is often the end rather than the start. Something with a barline hinting at phrases, like
Cm: ...V7 i | VII III... gives a bit of context where
i VII III could make sense.