Cloning checklist for cloned issues works out of the box.

Please note that cloning checklist in subtasks (when the issue is being cloned) works only if "Save checklist data to Jira custom fields" is enabled (vote for ACJIRA-2063)

Please note that cloned checklist takes precedence over default checklist. It means that for issues cloned with non-empty checklist, default template is not applied.