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.

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The other Pokemon in Jagged Pass are Numel and Machop.

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Numel and Machop are both also in Route 112 and Fiery Path.

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Route 112 has no other Pokemon.

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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.

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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.