So I've been thinking, having finally decided to join the great forces of Chaos (Praise be unto Khorne and Big T), how... well chaotic is chaos gonna be? Is there gonna rewards for SINDRI'ing your way up the ladder? Will our War Council reflect that? How about screwing over legions dedicated to other Gods (post-launch), or are we all united closer to the Heresy than the Black Crusade tabletop?

(The following is joke dialogue, you can't string me up yet while we are Chaos Undivided at launch.)
Because honestly I feel rewarding me for betraying the Slaaneshi's and Nurglites would be a massive immersive bonus that would add to the gameplay experience.

While I take immense pleasure in the idea of debuffing Tzeentchian squads with my Nurgle Sorcerer, we have to take into account gameplay over lore and it would make playing as a Chaos Marine a dozen times less fun for most people.

I say we should be undivided, because if chaos acts as a unified whole, we may attain victory.

Everytime you screw over big time and lose a battle you can claim it was just as planned to betray your comrades.

As Malgaroth said, gameplay > immersion.

Im positive that rewards for screwing over or murdering other Chaos player will not be a thing in this game, and thats how it should be. If Orks wont be running around murdering each other to climb the social/power ladder they surely wont be stapling this community crippling feature on us either.

Usually when Chaos factions start killing each other is when Chaos loses the overall battle. Since friendly fire is on, you can do whatever you want to immerse yourself, but it will be just as effective as it is in the books (which is to say, it isn't).

You shouldn't reward deliberate TK'ing.

But I'm sure one or two 'accidental' in-character slayings will be in order if you catch a Tzeentchian sorceror constantly preaching over the mic to a pack of Nurglites...

How about, each chaos-character gets a secret to-do-list from time to time what he can do to gain his patron-god's favor. The to-do-list comes at irregular intervalls, contains random opportunities and is only valid for a short period of time.

For example:

For +1 favor of Khorne: Kill a Slaanesh team-mate within 2 seconds after he scored a kill. Becomes invalid after first fail.
For +2 favor of Khorne: Score first kill on an enemy during a mission. With a close-combat weapon.
For +8 favor of Khorne: Kill an enemy Hero before time is up.

For +1 favor of Slaanesh: Kill a Khorne team-mate within 2 seconds after he scored a kill. Becomes invalid after first fail.
For +2 favor of Slaanesh: Kill 2 enemies within 5 seconds.
For +6 favor of Slaanesh: Conquer an enemy outpost before time is up.

For +1 favor of Nurgle: Kill a Tzeentch team-mate within 2 seconds after he scored a kill. Becomes invalid after first fail.
For +2 favor of Nurgle: Survive for 10 seconds after getting hit by a Heavy Weapon.
For +7 favor of Nurgle: Kill X enemies in a row without using a Heavy Weapon and without dying before time is up.

For +1 favor of Tzeentch: Kill a Nurgle team-mate within 2 seconds after he scored a kill. Becomes invalid after first fail.
For +2 favor of Tzeentch: Kill 2 enemies with one spell.
For +9 favor of Tzeentch: Kill player X before time is up.

For +1 favor of Chaos Undivided: Kill an enemy veteran.
For +2 favor of Chaos Undivided: Kill an enemy Elite or Hero.
For +4 favor of Chaos Undivided: Complete X Chaos-missions before time is up.

Of course, for every +1 favour gained with one God of Chaos, you automatically lose 0.2 favour at every other God of Chaos...

Getting in the Nurgle good books, by screwing over the other gods?
I can live with that.
And the glory of Father Nurgle.
I can live with that as well.