Permissions
Using Email This Issue requires users to log in. Anonymous users cannot access it and cannot use its features.
There two type of permissions in Email This Issue:

Send Manual Email Permission

By default, the Email button is displayed for all logged in Jira users in all issues. However, sometimes it is necessary to restrict access to this feature to certain users.
To access this setting, go to the Administration configuration tab and choose Permissions to Send Emails Manually under the PERMISSIONS menu item.
If the the above option is enabled, all users may send emails. However, if the option is turned off, Jira Administrators may grant permissions in the Jira Permission Schemes.

Send Issues in Email Permission

In this case, Permission schemes contain a permission type called Send Issues in Email that can be configured as a regular Jira Permission in the usual way. Users being granted this permission, are able to use the Email button and Email Screen. Unprivileged users may not access the Email screen.

Permission to Configure Email This Issue

To access the configuration screen and the Emails menu in the top navigation bar of Jira, users must be Jira Administrators or Jira System Administrators.
Future versions of Email This Issue will declare a new Global Permission type so that Email This Issue configuration may be delegated to privileged users.