Both Linoleic and Linolenic acids are very fragile and tend to oxidize easily.
For the Linoleic acid, you definitely want to keep the profile below 15%; Linolenic being even more fragile, is best kept below 7% and both together should not exceed 15% if possible. If they do, your soap would benefit from tocopherol (vitamin E) or some other powerful antioxidant. I have also heard that tiny amounts of BHA and BHT can help stave off DOS, but have not found a source for them in usable form yet.
Here are some oils High in the Lins --- I chose those that are either really really common, or examples of those that are really really high in one or the other. You can always go to Soapcalc.net to check the fatty acid content of your intended oils.
BLack Cumin Seed - 60% linoleic
Borage - 43% linoleic
Camelina Seed - 45% Linolenic
Canola Oil - 21% Linoleic
Cherry Kernel Oil - 45% Linoleic, 11% Linolenic
Cherry Kernel, 2nd Pressing, 40% Linoleic
Coffee Bean Oil(green or roasted) - ~39%
Corn Oil - 51% Linoleic
Cottonseed - 52% Linoleic
Cranberry Seed - 37% Linoleic, 32% Linolenic
Evening Primrose - 80% Linoleic
Flax Seed(Linseed) - 50% Linolenic
Grapeseed - 68% Linoleic
Hemp Oil - 57% Linoleic, 10% Linolenic
Kukui Nut - 42% Linoleic, 29% Linolenic
Loofa Seed Oil - 47% Linoleic
Oat Oil - 39% Linoleic
Passionfruit Seed Oil - 70% Linoleic
Peanut Oil - 26% Linoleic
Perilla Seed - 56% Linolenic
Pomegranate Seed Oil - 78% Linolenic
Poppyseed oil - 69% Linoleic
Pumpkin Seed Oil - 50% Linoleic
RBO - 26% Linoleic
Rosehip oil - 46% Linoleic, 31% Linolenic
Sacha Inchi - 35% Linoleic, 48% Linolenic
Safflower Oil - 75% Linoleic
Sesame Oil - 43% Linoleic
Soybean OIl - 50% Linoleic
Sunflower Oil - 70% Linoleic
Walnut oil - 60% Linoleic
Wheat Germ Oil - 58% Linoleic