How can i get rid of a flaky dry skin rash on one of my eyelids?

Topical corticostero: Topical low potency corticosteroids such as over-the-counter Hydrocortisone 1%. Also, consider moisturizing soaps and shampoos.

Eyelid rash: You description is most consistent with an allergic reaction or an eczematous rash. Both would respond well to Hydrocortisone creme 1% twice daily to rash. Since other issues can cause eyelid skin rashes, i would see a doctor prior to initiating therapy.