Why does my cat have flakes only on her lower back?

Usually because she can’t reach it. Cats normally distribute the natural oils in their skin across the coat by grooming, and a cat who can’t twist to reach her lower back, rump and tail base stops distributing oils there. The skin dries, dandruff develops, and sometimes the coat in that area becomes greasy or matted alongside the flakes. The two cat populations this happens to most are senior cats with arthritis and overweight cats. Brushing those specific areas for her does the work she can’t do herself.

When to call a vet: if your cat used to groom her whole body and recently stopped reaching her back half, that’s worth a vet visit. Arthritis pain is often treatable.