Dep Clone for Jira addon is an advanced solution for cloning single issues, a bulk of issues, epics or template projects in Jira. You can clone comments, subtasks, and more content.
You can easily clone your checklists with Deep Clone addon as well!
For that - add “Checklists” custom field following this instruction "Checklists" Custom Field and use it as additional storage for your checklist data.
When cloning Jira Issues - your checklist data would be cloned along with the custom field.