Can you actually field an army of monkey's?
Sounds funny.
Anyway, you can represent a bunch of the legions in the chaos codex pretty well if you ignore tabletop effectiveness.
You can mark all units to follow a specific god and use cult units for that god, e.g. Berzerker's with Chaos Space Marines that have the Mark of Khorne. Thousand Sons should take as many psykers as they can. Just take whatever fits with the chaos god of your choice really.
Undivided armies can be represented too:
Word bearer's should use Dark Apostles, Possessed, and a variety of marked units. Anything with the Daemon rule would fit in really.
Iron Warriors should have a load of tanks, Obliterators and a Warpsmith. One full unit of Obliterators, two daemon engines and a few Hellbrutes alongside some basic Chaos Space Marines would look good. They're meant to have fluffy loadouts for their squads too (I think it's a meltagun and lascannon) so there's that too.
Black Legion should take everything. They have their own supplement, and I think that Chosen are basically their fluffy unit. Have them be led by a Lord or Daemon Prince if you want. They represent all of chaos, so all of your marks, all of your Daemons, absolutely everything should be taken to excess. Sounds fun doesn't it?
Alpha Legion is all about infilitration, secrets and cultists (That form their information network). They're like the NSA of Warhammer. Sneaky guys, who you COULD take a Huron Blackheart counts-as in order to get the Deception Warlord Trait. That'd be a fluffy rule. Ahriman gives it to you too, but it's up to you whether you want to be lead by a counts-as Huron or counts-as Ahriman.
Night Lords (Whom I am most familiar with) are a broken legion, more than any other legions it seems. It's also kinda hard to agree on what exactly is fluffy for them, although everyone can agree on them not often having marks of chaos, having a affiliation for Raptors and not using daemons. I say this because recent books have portrayed them as "desperate" whereas older fluff simply presented them as non-daemonic.
Krieg Acerbus leads the biggest Night Lords legion, which is also the most chaotic, so his warband would involve anything in the chaos codex.
Generally, they aren't very chaotic though. You could think of them as a chaos legion that would take anything that they chaos codex has in common with the space marine codex.
So your Predators, Vindicators, Rhinos and Land Raider are your tanks. Cultists, basic Chaos Space Marines, Raptors, Havocs, Terminators, Bikers, Dreadnoughts (Not Hellbrutes, but the older models used as a Hellbrute), Lords and Sorcerors are what you should stick to if you want the "Desperate" type of fluff. You could again use a Huron counts-as(Described under Alpha Legion) to provide the Deception trait, as they have done a bit of sneaking in their time. You also shouldn't ally with Daemons, although that's kinda implied...
You should remember that conversions can be used for certain unit entries too though, like two Night Lords holding multiple heavy weapons that represents an Obliterator. See the following link for more counts-as Night Lords goodies:
http://www.bolterandchainsword.com/topic/172506-night-lords-18th-battle-company/
The more chaotic type of Night Lords warband still probably wouldn't ally with Daemons, although they could take anything that the desperate-Night-Lord-type warbands can take, and more. I say this because the 3.5 chaos codex allowed you to field such an army of Night Lords, and allowed you to take everything except Marks of Chaos and almost all Daemons (Furies and Daemon Princes were allowed). So if you steered clear of marks/cult units, or represented them differently (See above link, use shields for plague marines, etc.) you should be fine.
Loads of the legions are broken up, or still intact to certain degrees too, which you could represent. World Eaters, Thousand Sons and Emperor's Children are all broken up to varying degrees.
Thousand Sons can still muster up about half a chapters-worth of marines when under Magnus. And there was a crusade of Fire involving 50,000 Berzerkers. So it kinda differs depending on the circumstances.
Alpha Legion warbands operate in cells, so would be small enough. The Night Lords are all over the place, with no-one to reunite them. The Iron Warriors are an odd one, still capable of fielding hundreds of marines (And occasionally allying with Daemons, although they aren't known for it) though they also fight against other warbands of their own legion.
I'm not too sure about the Death Guard, but I do know that the Black Legion and Word Bearer's still have some form of organisation. When Abaddon calls, the Black Legion comes to heel in it's entirety, or at least most of it. The Word Bearer's have a Dark Council that organises the entire legion. Each member is a Dark Apostle (Or Lord, whatever) that has his own host, which can be the size of a space marine company, or larger than a chapter, which they control.
Honourable mentions go to the Red Corsairs, a former space marine chapter, now gone rogue. They're led by Huron Blackheart, and by taking in freshly turned space marines, they've managed to boost their numbers to almost the size of a pre-heresy legion. They could be represented similarly to the Black Legion, but with an emphasis on vanilla chaos space marines to show off how many Space Marines they have. Being led by Huron would also convey fluffiness.
There's also a bunch of smaller, unique warbands that went rogue after the heresy that are covered in the Chaos Space Marine codex, but if you aren't interested in what I've covered so far, then they won't pique your interest.
