The promoted builds plugin provides an API for a promotion but not for the list of promotions.
Available:
<host>/jenkins/job/<project>/<build number>/promotion/<promotion name>/promotionBuild/<promotion number>/api/xml
Should be available:
<host>/jenkins/job/<project>/<build number>/promotion/api/xml
<host>/jenkins/job/<project>/<build number>/promotion/<promotion name>/promotionBuild/api/xml