Flaking is definitely normal, but a week isn't the end of the process. Depending on how deep the peel was, your skin can keep flaking for another week or even two, so be prepared for that. The main thing is don't pick at the flaky bits with your hands - it'll slow down healing and could leave scars.
Make sure to use a gentle moisturizer without acids and retinols, apply it 2-3 times a day to damp skin. Sunscreen is a must - even if it's cloudy outside. While active flaking is going on, avoid hot water, scrubs, alcohol-based toners, and any irritating products.