Amazon Private Label takes several steps to ensure that the products they sell are safe and of high quality, including requiring sellers to provide detailed product information, enforcing strict policies and regulations, using specialized fulfillment centers for perishable goods, and soliciting customer feedback.
If you have mentioned the product expiration dates on the backend of your listing then Amazon will make your listing inactive after the expiry date or else if several customers complain about the expiry date then Amazon will automatically remove your product and let you know.