The Kangs are one of the several disparate factions inhabiting Paradise Towers (the Caretakers, whom I have previously referenced, being another). And, although it is not immediately obvious, the Kangs are also the best adjusted and generally together of the Paradise Towers factions. Which might say a thing or two about the current state of Paradise Towers.
The Kangs are roving bands of teenage girls who engage primarily in graffiti (wall-scrawl) and gang warfare. Their parents and brothers all left to fight in some war (with the exception of Pex, but he's a Cowardly Cutlet, so don't mind him) and never returned. In their absence, the girl-children went a bit...feral. And then developed complex and largely effective social structures. And really fabulous 80s hair.
There are three flavors of Kangs, if you will: Red Kangs, Blue Kangs, and Yellow Kangs. I read once that these were possibly allegorical representations of the three major political parties of the UK, but as an American who knows nothing about these things...I know nothing about these things. Except that I generally share Tolkien's opinions on allegory (he's agin it). In any event, the three colors of Kangs are mutually opposed, and derive a lot of their identity from their particular allegiance. For instance, the battle cry of the Red Kangs is:
"RED KANGS RED KANGS RED KANGS ARE BEST!"
As far as political slogans go, you have to admire that one for its straightforwardness and lack of double-talk. But Kangs tell it like it is. The Yellow Kangs are having the worst of it - in fact, when we enter the story they are down to a single member. Poor old Yellow Kang the Last...
Although the three colors of Kangs are engaged in perpetual gang warfare, they have a sort of mutual respect for each other. They are all still Kangs, as opposed to Resis (elderly cannibalistic residents) or Caretakers (servants of the sinister Cleaners). They would never dream of aiding each other, but Kangs do not kill other Kangs, and they mourn each others' passing. As they say at the funeral for Yellow Kang the Last (yeah...she didn't last long):
"Hail Yellow Kang the Last. Hail the Unalive. Though Yellow of color, she was brave and bold as a Kang should be."
This raises an interesting point. The Kangs have managed to evolve into a real, functional society (albeit an amazonian one). They have funerals - they honor the dead. They have ritual, hierarchy, honorifics (their names are all taken from items in their environments: Bin Liner, Fire Escape, etc.) When working together they are extremely effective. They have their own myths and legends, and know more about what is actually going on in the world of Paradise Towers than anybody else. It's a child-developed culture that has grown into something real and functional, rather than a broken adherence to pre-existing patterns that no longer have any relevance or meaning. The Kangs have evolved into something new, something adapted to the world around them, and so they are the healthiest and best adjusted of the inhabitants of Paradise Towers. They also have an incredible fondness for fizzy drinks.
The Kangs also have the best language. You may have noticed some of it. I sometimes describe "Paradise Towers" as "Doctor Who does Language Change: Part III." Part I is "the Face of Evil" with the Tesh and the Sevateem, and Part II I've already discussed with "State of Decay" and its gross misapplication of Grimm's Law (for a worthy cause). I find the treatment of Language Change in "Paradise Towers" to be the most believable and satisfying, for a couple of reasons. Firstly, it is almost entirely lexical. The other two examples are Sound Change, and inherently problematic because (neogrammarian) Sound Change is regular and exceptionless, which the examples given aren't. But semantic drift and semantic shift operate sporadically and idiosyncratically, so it's much harder to do wrong. It is also entirely believable to have happened within a single generation, so it's the right type of language change for the context. The conventional wisdom in the linguistics community is that children do not learn language - they create it anew. And conventional wisdom among, well, me, is that the purpose of language is not to facilitate communication, but to impede it. Language is for separating one group from another, for aiding in identity formation and reinforcement. And so it is with the peculiar but strangely natural speech of the Kangs. It is a mode that has evolved with them, and helps to define them as Kangs (and it is common to all three colors). And it's just cool sounding.
For the record, the word Kang itself is based on "gang," but used entirely differently. It refers to the individual members, not to the organizations as a whole.
As far as I'm concerned, "Paradise Towers" is a perfect episode of Doctor Who. It is a bit hard to get into because of the extreme 80s-ness of the Kangs in particular, but once you get a good look at them they are magnificent. When I write my Gilbert and Sullivan operetta of Paradise Towers, the Kangs will be the female chorus, and Bin Liner will be the Subrette (Bin Liner and Fire Escape ~ Pitti Sing and Peep Bo).