Where did the list of flagged message go in Mavericks Mail?
I had this problem -- the "Flagged" folder disappeared from the Mail app and no longer contained any flagged messages, even though I could see that my messages still had flags if I logged into the iCloud website and looked at them there.
For me, the solution was to rebuild my Inbox in the Mail app. Select the mailbox you want to rebuild ("Inbox" in this case), go to the Mailbox menu, and select "Rebuild" at the bottom of the menu. It could take a minute or two, depending on how many messages you have. Suddenly Mail recognized all the flags again, and my Flagged folder re-appeared with my flagged messages in it.
Select the inbox in question, then the mailbox menu and "rebuild". We had this issue on 3 machines in my office and length rebuild was required. I've noted the flags show up if you surf to one of the flagged emails...it's as if "touching" the emails is required for the data to be triggering the flag functionality...rebuild must have the same effect.
The flagged message folder isn't missing on any of the 5 Macs I have upgraded to 10.9 so I'm concluding that the folder isn't intentionally being removed as a matter of design.
I suspect you have some database corruption or another error (perhaps gmail two factor authentication) causing the missing folder.
Have you reached out to Apple support? They typically offer free support within 90 days of any "purchase" and it would be interesting to see how they handle a "purchase" for a free app.