I'm 99% sure this cant be done with a standard flat file destination as the columns are actually bound in the connection manager rather than the destination for a start.
You might be able to achieve it with a script component (even then I'm not so sure).
The only option I can think of is to add a couple of "dummy" fields to the end of the connection manager and use them as needed (you'd have some blank fields when they aren't used). To do this you'd need to remove the header row option in the destination connection manager and then fabricate a row to add at the top of your dataset to add the column headers in that way.