How to change the default date format in Rules?
Try to use what you have defined as the format for short / medium / long format in your Drupal date settings, using either of these tokens:


[commerce-order:field_delivery_date:value:short]
[commerce-order:field_delivery_date:value:medium]
[commerce-order:field_delivery_date:value:long]


However, since your date seems to be a data range, you may have to enable the Entity API module and its "Entity tokens" sub-module to access the date values.

Also, be aware that Entity tokens replaces underscores  (= "_") in the tokens names by dashes (= "-"), so in your case "field_delivery_date" becomes "field-delivery-date". And with that, this is how it should look like:


[commerce-order:field-delivery-date:value:short]
[commerce-order:field-delivery-date:value:medium]
[commerce-order:field-delivery-date:value:long]