Using code field to display field from referenced entity
Use views and a contextual filter with the entity reference relationship you have created. Use EVA to get the block as field in Display Suite.

Display Facility nodes, choose the right format (I'd go for Unformatted List). Create the relationship in the right panel choosing two references, one that points from Facility to User, then one the points from User to Telephone using the first relationship.

Use contextual filters, provide default value Content ID from URL, validation criteria Facility content type.

Add a field "Title" using the second relationship. Now you have a block that you can publish on your page. If you need it as field in DS, use EVA to create it.