The answer depends on what kind of account you are using.
ActiveSync/HotMail
ActiveSync simply does not sync "Sent Mail". This is a limitation of ActiveSync. It may be fixed in future ActiveSync implementations.
POP3
POP3 is not a synching protocol but a a one way Server->Client protocol which mean there is no uploading typically done. There are some POP3 servers that allow this in a non-standard way, but FlexMail does not support this. You can BCC sent emails for the account so that it goes to you and you can setup a rule on the desktop to put those into his Sent folder - that's the standard method.
IMAP
This is a basic feature of IMAP. Simply go into the Server Folders dialog and choose what is the Sent folder. Then make sure its set to Upload email to that folder.