How to grant users permission to Close Issues in Jira
Problem
At times you might want to allow users to close their own issues, however granting the Close Issues still doesn't make them able to see the close button.
Cause
The reason is that other permissions are also necessary for closing an issue, since it involves setting a resolution and transitioning the issue to a "Closed" status.
Resolution
This does not apply to Service Management customers. See - JSD-40Getting issue details... STATUS for more information on that.
Grant the user (or group of users) the Resolve Issues and Transition Issues project permissions.