The "Jenkins Mailer Plugin" allows you to define a post build action for sending mail notifications. You can also use the "Jenkins Email Extension Plugin" plugin https://wiki.jenkins-ci.org/display/JENKINS/Email-ext+plugin if you need more control over the email itself.
To customize the recipients from a text file, you would set the recipients to a Jenkins variable (like $MyRecipients). Now, to populate that variable from a file, you could use the "Environment Injector Plugin" https://wiki.jenkins-ci.org/display/JENKINS/EnvInject+Plugin.
There you can specify a properties file to load as an Action in your step. You will want to use an absolute path to the file (like /jenkins/maillist), and make sure the content of that file follows regular shell syntax for setting properties. It should be something like:
MyRecipients="address1@test.com address2@test.com addres3@test.com" I haven't tried this specifically, so I hop there are no syntax errors here, but the general approach should work. Not sure how well that will scale though. If you intend to send mail to many users, you may instead want to implement a shell script to call that just does this outside of jenkins.
Sven