Dep Clone for Jira add-on 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 the Deep Clone add-on as well.

For that - add the “Checklists” custom field following this instruction "Checklists" Custom Field set up 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.