Vivisectionist gets 1d6 sneak attack at 1st level and every 2 levels after, and is said to stack levels with other sources of sneak attack.
...But how does that work when the other source doesn't grant it at the same rate? Eldritch Scoundrel gets 1d6 at 3rd level and every 4 levels after. Would a multiclassing of the two use the slower rate? The faster one? Whichever you got into first? Would you just count them up separately instead of adding the levels together?
It just means that you add the amount of sneak attack you do have together for your total sneak attack. So if we say you are a 3rd level Eldritch Scoundrel and a 3rd level Vivisectionist alchemist, you have in total 3d6 sneak attack (1d6 from ES, 2d6 from Vivi.)
You calculate separately how many sneak attack dices you get for your x level in vivisectionist. Then calculated how many sneak attack dices you get for you y level in eldritch scoundrel. Then you add the dices together.
For example. A eldritch scoundrel 5/ vivisectionist 5 would get +1d6 from the scoundrel levels and + 3d6 from the vivisectionist levels for a total of +4d6.
Add the dice together for each class granting sneak attack, unless the class explicitly tells you something else.