Single Target
Unlike Legion, Battle for Azeroth Affliction generally follows a pretty basic priority list after your opener.
Things like racials and on-use trinkets on CD
Haunt if talented
Maintain Shadow Embrace if talented
Do not let Agony fall off
Do not let Siphon Life fall off if talented
Do not let Corruption fall off
Phantom Singularity on CD if talented
Vile Taint on CD if talented
Dark Soul on CD if talented
UA if you are at 5 Shards
UA if UA is not on the target or will expire before the cast finished. Skip this line if you are pooling for Darkglare, more on this later.
UA once before Deathbolts. Skip this line if you are pooling for Darkglare, more on this later.
Deathbolt on CD
Shadow Bolt

The rotation changes slightly leading up to your Darkglare Cooldown. You should always try to have 5 Shards when Darkglare comes off CD to maximize the value of your primary cooldown. This generally means you want to stop spending Shards about 45 seconds before Darkglare comes off CD. You should still prioritize not capping Shards, so if you hit 5 use a UA.

Shortly before (the time it takes you to execute all of the actions before your Darkglare, ideally) your Darkglare comes off cooldown you want to change how you prioritize your actions.

Dark Soul if talented and off CD
UA 5 times, or as many times as you can up to 5. If Vile Taint is talented, make sure to leave 1 Shard available for Vile Taint.
Vile Taint or Phantom Singularity if talented
Darkglare
Deathbolt if talented

OPENER

Precast Haunt if talented or Shadow Bolt if not
Agony
Siphon Life if talented
Corruption
Dark Soul if talented
Racials / On-use Trinkets
UA as many times as you can, up to 5. If Vile Taint is talented, make sure to leave 1 Shard available for Vile Taint.
Vile Taint of Phantom Singularity if talented
Darkglare
Deathbolt if talented
Proceed to normal priority

Azerite/Tips
Drain Life trait
Cascading Calamity
Make sure to dump your UAs when the boss is near death so you don't end the fight with wasted Shards