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.

I found high-sugar foods to be one of my many triggers. Never really understood why...