Reposting the FAQFAQ wrote:
Channel Energy: If I have this ability from more than one class, do they stack?
No—unless an ability specifically says it stacks with similar abilities (such as an assassin's sneak attack), or adds in some way based on the character's total class levels (such as improved uncanny dodge), the abilities don't stack and you have to use them separately. Therefore, cleric channeling doesn't stack with paladin channeling, necromancer channeling, oracle of life channeling, and so on.
Like I said previously, you apply the instances of sneak attack separately.
Lets say you were a unrogue 1/slayer 3/wizard 3, you would have two instances of sneak attack 1d6. If you attacked a target and met the requirements for applying sneak attack, you would deal 2 instances of +1d6 precision damage or 2d6 overall. However, since neither class grants you 2d6 sneak attack, you would not qualify for arcane trickster, since you only have 1d6 sneak attack.
This is incorrect. If that were the case then we would not need the wording to say that it stacked to begin with as 2d6 SA and 1d6+1d6 are the same. If it was intended only to make a difference for prerequisites then it would say as much. As is, there is literally no mention of prerequisites in that FAQ.