Delivery Date plugin is not showing up on Checkout Page

Do you have configurated all plugin settings and the delivery fields isn't showed on the checkout page ?
A possible issue is that you hasn't set the "Order Processing method" in a WooCommerce Shipping method.

Check if in your order processing method configuration and there is in the metabox "Shipping Method" is empty.

Click on "Manage shipping zone" to set your method in the shipping method.