There's no reason for FlashFXP to identify itself. The server doesn't need to know what client you're using, so why tell it?
I don't know about most users but personally the ftp server operator has no business knowing what ftp client you're using.
If a user wants they can fake their client, make it anything they want.. hows that sound
From the Site Manager / Advanced / Perform on connect, add the following text
CLNT <whatever>