Who can set due date to a Checklist item?
Admins of the Board, members who have permission to create Sections and Tasks, and members who have permission to edit Tasks within a board can add due date to checklist items.
How to set due date to a Checklist item?
- Click Tasks in the left menu.
- Navigate to the required Board and Task.
- Click the task, to open task details.
- Hover above the Checklist item and click the
icon seen in the right end of the checklist input box. 
- From the date picker, select the due date.
- Enter the due time in the input box or select a time from the dropdown.