There may be two effects going in parallel, but: for chronic migraine sufferers reducing blood pressure can be effective in reducing attack frequency, and ketogenic (and other very low carb diets), can reduce blood pressure frequently. Blood pressure being a big factor in the effects of vasodilation.
Honestly, I've long dismissed the claimed benefits of ketogenic diets like 'reduced inflamation' as... minor and uninteresting. A few weeks into a low-carb diet for my migraines and my sedentary butt is suddenly running and with my untrained knees never having felt better. I would not be shocked if there were other beneficial effects of ketosis on migraines.
Honestly, I've long dismissed the claimed benefits of ketogenic diets like 'reduced inflamation' as... minor and uninteresting. A few weeks into a low-carb diet for my migraines and my sedentary butt is suddenly running and with my untrained knees never having felt better. I would not be shocked if there were other beneficial effects of ketosis on migraines.