There are two options in ESILAW 360 for entering a flat fee, they are.
Option #1:
Post a time entry with zero hours and enter your lump sum in the Fees section (see example below).
Option #2:
Go to Create Pre-bills & Bills and add Flat Fee on a the bill (see below example). In the narrative make sure to put notes for the flat fee. Once finished hit the Save & Close button.
You should now be able to use these two methods for entering a flat fee.