By order of the Lady of Pain, there will be but 15 factions in Sigil. Organize thy colors by a fortnight hence - or die.
I know this does not mean colors exactly, but do you describe some factions with a specific style, with faction members wearing colors typical for them - when they want to show they belong to a certain group.
Probably that doesn't work for Anarchists, Bleakers, Sensates.
Mercykillers - I think Red; Hardheads - Blue, Red, Gold; Doomguard - Black, Red?; Dustmen - Black, Grey, White, Purple; Indeps - Gold and Purple? (like the Bazaar)
What about the rest of them?