This cake is primarily relying on the eggs and sugar for structure. Keep in mind too the chocolate also contains cocoa powder, so you have some hidden dry ingredient there, which will hydrate and thicken when exposed to the liquid in this recipe. The hazelnuts will mostly provide flavor and maybe hold onto some extra moisture to prevent the texture getting too eggy or rich is my thinking. So while any substitution will result in a different end product, you probably don't have too much to worry about.
Realistically, you could substitute with regular cake flour without risking much. Using wheat flour might lighten or dry the overall texture a bit, but not severely. The main issue I perceive is that wheat flour doesn't have a flavor that's particularly recognizable. Similarly, you could use a starch, but any starch would not contribute flavor, and could cause dry, gooey, or gummy texture. Wheat flour is definitely a better option than starch.
For the flavor aspect, I'd be more inclined to toast and grind some oats to add a little nuttiness without adding anything too identifiable.
Cornmeal could also be an easy sub which would provide some nutty (albeit distinctive) flavor. You can also use ground coffee, for all or part, to coordinate with the chocolate and chili flavors. Other flavorful options would include various seeds (poppy, sunflower, and pumpkin come to mind). Seeds might be the best direct substitute due to the similar fat/protein/carb profiles, but there's plenty of variation, and you're unlikely to find a perfect match, and of course the flavors are both different and recognizable.
Most importantly, make sure you double-check with whoever has the allergy to make sure your sub is actually safe!