In order to use Cloudinary's images as featured images, make sure to upgrade to the latest version of Cloudinary's WP plugin.
You first need to insert an image to your post using Cloudinary's media library and to save a draft of your post. Then click on the Set featured image link of WordPress. This will open the WordPress Media Library that now includes also the Cloudinary images you previously inserted into your post. Select the image you want and that's it.
The featured image will be uploaded using Cloudinary's generated transformed version of your images, and delivered through a fast CDN.
Another option is to go to your existing WordPress Media Library and synchronize your image to Cloudinary by hovering the image and click on Push to Cloudinary. The image will be synced to Cloudinary and you can now select these images as a featured image directly from your WordPress Media Library while being delivered using Cloudinary URLs.
In addition, you can use 3rd party plugins like Featured Image via URL. With this plugin, you can easily enter any URL of your Cloudinary images (including transformed ones) to set it as a featured image for your post.