Hi Amy,
Thanks for reaching back out to MailChimp support. I'll be more than happy to provide some clarification on how to get those images to show up with the summaries of your posts.
In order for those RSS tags to pull images in those images will have to present in the feed. Feedburner is definitely one of those "popular blog softwares" which would just be certain feed providers many people use, and it may be the case that they allow you to add images to the feed within the summary of each post. It would be necessary to reach out to Feedburner's support team in order to get assistance with setting up the feed to include images for each summary.
If those images were present in the feed itself, in each summary, however, then using that *|RSS:POSTS_HTML|* tag should work to bring each image in along with each summary.