From my understanding, you don't do it through FLICA, but rather PBS. When you make your bid for the next month, select 'Avoid Pairings' and input the employee number of the captain you wish to avoid being paired with.

If you have been awarded a line for the month, and have a pairing with a captain you prefer not to fly with, the best you can do is try and drop that trip through FLICA. PM me if you have any more questions.