How do I override/theme Views REST Export display field?
Here's one option: 

Add a new relationship in the view for the field (field_feature_image in your case)

Add new field for "File: URI" using this new relationship

Use the File URI formatter, and also enable the "Display the file download URI" option

This method may not be ideal for fields with multiple values. I am still working out the best method to do that using the core tools in Drupal 8.