Shopify does not have a standardized way of storing delivery date or times since those details are added by other apps. However, in most cases, apps add them as "Cart Attributes" in the order details.
You can display those details in the documents by following the instructions below:
Login to OrderlyPrint (Shopify admin -> Apps)
Go to the Settings -> Document design page.
Go into the Options and Formats section of the editor
Enable the checkbox Show cart/note attributes
This will then include any delivery dates, times or other additional information from the orders, in the documents Notes section.