When using the CloudBees folder plugin, clicking on the Promotion Status link for a job will not show the "Build" icon unless you are logged in as an administrator. Similarly, if you attempt to run the Promotion on a slave that is restricted to a folder, the job will become permanently queued.

Since the Jenkins team owns both of these plugins, they should work together. According CloudBee's own documentation, the Promoted Builds plugin needs to make use of a particular extension point to function with the Folders plugin: http://jenkins-enterprise.cloudbees.com/docs/user-guide-bundle/foldersplus-sect-controlledslaves.html.