Set the contractor up as an employee in FlexiTime. Please see this article for details on creating a self-employed contractor.
If they have User Access, 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 new pay code called Job Based Pay - Daily. This should have the same settings as the regular Job Based Pay pay code, except that instead of Hours as the units you should choose Other and enter Days as the unit label.
Create a Charge Type for invoicing the work, but with the units set the same as on the pay code.
Create a new Work item and link it to those new pay codes and charge types.