Set the contractor up as an employee in FlexiTime. Please see this article for details on creating a self employed contractor.
Select the employee's User Access tab and remove the tick from Show Graphical Timesheets. Without start and end times there's nothing to show on the graphical timesheet so the employee only needs to see the time summary tab.
Create a "Job Based Pay - Daily" pay code the same as the regular "Job Based Pay" pay code, except that instead of Hours as the units choose Other and enter "Days" as the unit label.
Create a Charge Type for invoicing the work, but with the units set as for the pay code.
Create a new Work item and link it to those new pay codes and charge types.