Curious what advice people have on incorporating flat chords (such as bIII, bVI, bVII) in their songwriting.
A lot of 60s/70s pop rock uses bIII between I and IV -- so, I - bIII - IV. See: Starman by Bowie, Back in the USSR by Beatles.
bVI - bVII - I is a really common usage of bVI and bVII together. Quick example http://www.hooktheory.com/theorytab/view/links-awakening/koholint-island-theme
bVI and bVII are also commonly used to modulate into a major/minor key that's nearby.
bII can subsitute ii in a jump to V and give a more distinctive pull, or used to transition smoothly between itself and bVI (since they have that 5th apart relationship.)
bV is good for tritone subsituting I, among other things. Especially in Jazz.
♭III, ♭VI and ♭VII occur freely in major/minor mixture. ♭VI♭7 = subV7/V has the same notes as Ger56. (related is the Tristan chord, ♭viø7 = subiiø7)
Slash chords introduce these flat chords easily in both major and minor keys, in particular ♭II7d [D♭M7/C], which usually comes from II7d, forming V24/V - subV♯7 - i; ♭♭iiiø7 - ♭II7 is also common. Other chords are Iø9 [G♭/C or C7♭9♭5] and I479 [B♭/C].
i can lead to ♭V46 directly. ♭II - ♭V and ♭VI - ♭V are also possible.
In minor it is possible to use i - ♭I, i - ♭ii♭7, ♭VII - ♭iii or even i - ♭v to modulate to very far keys.
Conversely iii and vi, coming from the parallel major, are used in minor key to modulate to the mediant or simply substitute other chords. All these usages of chromatic chords deviate heavily from tonal harmony.