As of Oct 10, 2017, the Sites@Duke service, through which OIT administers thousands of Wordpress sites to the Duke community, supports shortcode for embedding media from the Duke Digital Repository.
Sites@Duke (and indeed Wordpress.com and many other CMSes) does not permit users to add <iframe> tags to their posts or pages, though those tags are standard for embed features for services like YouTube, Soundcloud, and the DDR. Shortcodes have become the method of choice to support embedded media in Wordpress, essentially defining a whitelist of services and some shorthand code for users to insert the desired content into their posts. DUL reached out to OIT to request this feature on Jul 21, 2017 (see thread) and OIT moved quickly to support it.
Here's an overview of how Sites@Duke now integrates with DDR embedded media:
The service is built on the Duke Media Embed WP plugin
Duke Digital Repository is now one of five Duke services supported via shortcode.
Type [duke_media src=""] and paste in the DDR item permalink. Add width & height if desired.
The DDR embed feature renders for the object in the published page or post.