That does not look like any kind of burn to me, it looks like alopecia, though I'll try and think of some conditions that might cause it. Is the site sore, itchy or bothering the cat at all? Although the skin is darkened, it is hard, flaky or anything? From that pic, it does not look sore.
It might be worth getting some bloodwork done. Hypothyroidism does cause hair loss on the flanks that looks just like that, but the alopecia is usually symmetrical on both sides of the animal, and its fairly rare in cats.