Why don't WordPress featured images show in my feed?

Featured images don't get included in WordPress RSS feeds by default. If images are in your feed, we will detect that and display it.

There are plugins that can insert featured images into your feed such as the one below:
Your WordPress theme must also include the following code in the functions.php file.
add_theme_support( 'post-thumbnails' );
You can seen  in this example that this feed has featured images showing up.
Feeds that contain featured images will show up in the emails people receive.