Dep Clone for Jira is advanced cloning of 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.
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.