ROTATION:
For general conception, take a look at the overall priority list:

On 1 -2 targets:

Keep up  Immolate  on the target 100% of the time.This debuff can be put with  Cataclysm if you have this talent. .
Chaos Bolt to avoid soul fragments overcap.
Cataclysm every cooldown (if you have this talent)
Channel Demonfire every cooldown (if you have this talent)
ON 2 TARGETS:  Use Havoc on the second targets as often as you can savin up 2-3 soul fragments in advance and at least  1 stack of Conflagrate in the moment of usage. While Havoc  is active you need to cast not less than 3 Chaos Bolt and 2 Conflagrate.
Soul Fire every cooldown (if you have it)
Chaos Bolt
Conflagrate, can be used while moving but never let 2 charges be up
Incinerate to generate Soul fragments.


Cooldowns management:

Summon Infernal –  a pretty simple burst, in most of the cases you should use it every cd. When playing with  Dark Soul: Instability, you should use this ability every cooldown,  but before using it make sure that your Immolate  was cast recently  and also you should have 4+ souls fragments. Try to use Во время действия этого бурста мы будем стараться использовать Chaos Bolt  while bursting as often as you can. It is important to generate soul fragments attentively.



When playing with  Grimoire of Supremacy and  Dark Soul: Instability, it is optimal to combine these 2 cooldowns when it is possible. The important factor in this situation is the fight duration.:

If combat lasts less than 190 seconds , use  Dark Soul: Instability  every cooldown.
If combat lasts  190-250 seconds hold  Dark Soul: Instability for the second Summon Infernal.
If the fight lasts  250-380 seconds, hold  Summon Infernal for the third Dark Soul: Instability.


A few rules for AOE :

Rain of Fire  is a bigger priority than  Chaos Bolt on 3+ targets considering that mobs will leave the range of an ability.
Rain of Fire  is a bigger priority than Chaos Bolt for Havoc on 5+ targets.
Immolate should be kept on up to 8 targets if they would live not more than 6 seconds..
Although  Immolate has less priority than Rain of Fire or Chaos Bolt.
Havoc is good to use on a pack of not less than 4 targets.
If Grimoire of Supremacy is taken and you Summon Infernal  on AOE and not on a single target then you should hold Havoc until the last 10 seconds of Summon Infernal. Cast Rain of Fire in the first 10 seconds to spend a lot of Soul fragments and in the last 10 seconds spam Chaos Bolt  while Havoc is active.
On 5 or more targets Havoc can be used for a fast soul fragments generation for Rain of Fire.


A few more  tips:

Abilities duplicated by Havoc, also generale soul fragments. It means that  Conflagrate  will also grant you one soul fragment. Havoc  can be cast on the targets under partial immune or minus damage effect for soul fragments generation.
Using  Cataclysm together with  Channel Demonfire  in m+ is very effective. Pay attention on your bursting cooldowns and try to to synchronize them.


Start of  combat:



Single target:

Battle Potion of Intellect + Incinerate 3 seconds before the combat.
Cataclysm for Immolate if you have the talent otherwise cast Immolate manually.
Conflagrate.
Summon Infernal.
Generate soul fragments without overcapping them. If their amount is close to 5 spend them on Chaos Bolt.
20 seconds before Summon Infernal ends  cast Dark Soul: Instability and use trinket if you have it.
Cast  Chaos Bolt as often as possible in these 20 seconds generating soul fragments with Incinerate and Conflagrate, spending stacks of  Backdraft on Chaos Bolt.


2 targets:

Battle Potion of Intellect+ Incinerate 3 seconds before the combat.
Cataclysm for Immolate if you have the talent otherwise cast Immolate manually.
Conflagrate.
Summon Infernal, Dark Soul: Instability  use trinket if you have it.
Generate soul fragments without overcapping them. If their amount is close to 5 spend them on Chaos Bolt.
20 seconds before Summon Infernal ends  cast Dark Soul: Instability and use trinket if you have it.
Use  Havoc on an additional target.
Cast Chaos Bolt, until you run out of soul fragments.
Cast Conflagrate
Try to cast  Chaos Bolt as often as possible while Havoc is on.
Cast  Chaos Bolt as often as possible in these 20 seconds generating soul fragments with Incinerate and Conflagrate, spending stacks of  Backdraft on Chaos Bolt.


Pets management:

The pet choice does not affect damage, you need to chose the pet according to the situation.
You should  play with Summon Imp in raid usually because it can dispel. Besides imp spends a bit more time to change the target.
In mythic keys you should use  Summon Felhunter that can interrupt casts.