First, this answer assumes that the chance of finding each level is the same. For example, Torkoal's encounter chance is 18% and can be any 1 of 3 levels (specifically 14, 15, or 16), so I assume that the chance of finding each level of Torkoal is 18%/3 = 6%.
Spoink is in only Jagged Pass.
source
The other Pokemon in Jagged Pass are Numel and Machop.
source
Numel and Machop are both also in Route 112 and Fiery Path.
source
source
Route 112 has no other Pokemon.
source
The other Pokemon in Fiery Path are not anywhere else, so you can't catch them in other places and then use species clause to catch Numel or Machop more easily.
source
I think this strategy maximizes your chance of finding Spoink. It's important that you go to Fiery Path, Route 112, and Jagged Pass in this exact order, because I think going Route 112 first lowers your chance of catching Spoink.
use a level 16 Pokemon and a repel to catch a Pokemon in Fiery Path. It's 15% Numel, 7.5% Machop, 12.5% Grimer, and 6% Torkoal. There's a 41% chance of encountering something that you must catch. When that happens, the chance that it's a Numel is 15/41, Machop is 7.5/41, and something else is 18.5/41.
catch a Pokemon in Route 112
If you caught Numel in Fiery Path, then you must catch a Machop.
If you caught Machop in Fiery Path, then you must catch a Numel.
If you caught something else, then it's 75% Numel and 25% Machop regardless of whether you use the repel trick.
After these 2 steps, the chance of having only Numel is the chance of catching something else in Fiery Path and catching Numel in Route 112, which is 18.5 / 41 * 75% = 111/328.
The chance of having only Machop is the chance of catching something else in Fiery Path and catching Machop in Route 112, which is 18.5 / 41 * 25% = 37/328.
The chance of having both is the chance of catching Numel and then Machop or catching Machop and then Numel, which is 15 / 41 * 100% + 7.5 / 41 * 100% = 45/82.
111 / 328 + 37 / 328 + 45 / 82 = 1, which means it's possible that I have not yet made a mistake.
catch a Pokemon in Jagged Pass. It's 55% Numel, 25% Machop, and 20% Spoink regardless of whether you use the repel trick.
If you have only Numel, then you must catch Machop or Spoink. There's a 45% chance of encountering something that you must catch, so when that happens, the chance that it's a Spoink is 20/45.
If you have only Machop, then you must catch Numel or Spoink. There's a 75% chance of encountering something that you must catch, so when that happens, the chance that it's a Spoink is 20/75.
If you already have both Numel and Machop, then you must catch a Spoink.
The chance of catching Numel and Spoink is (111 / 328) * (20 / 45) = 37/246.
The chance of catching Machop and Spoink is (37 / 268) * (20 / 75) = 37/1230.
The chance of catching all 3 is 45 / 82 * 100% = 45/82.
The chance of catching a Spoink with this strategy is the sum of the above 3 chances, which is 299/410, or roughly 3/4.
Also Camerupt has low speed and defense stats, which is probably bad for Nuzlockes. Torkoal and Ninetales might be better, but they can't learn earthquake or rock slide.
