Several breeds of dogs including bulldogs are prone to alopecia (hair loss) on their sides or flanks. Usually the hair loss is symmetrical and the skin will become darkly pigmented. When this is seen the dog should be tested for hypothyroidism (low thyroid). If the thyroid level is normal, then the hair loss is probably seasonal alopecia. There will be hair loss in the time of the year with shorter days and initially the hair will regrow in the time of year with longer sunlit days. Seasonal alopecia is usually progressive and sometimes the alopecia is all of the year. The disease progression can be slowed somewhat by diagnosing and treating all other skin conditions, omega fatty acid supplementation and
not over bathing. There is a treatment (melatonin) for seasonal alopecia that almost never
works. I have never seen a bulldog (many hundreds) successfully treated for this condition. It is best to just accept the bare flanks as a cosmetic issue.