Same here, i did deeper investigation:
It just affects the IPhone 5s. I've an IPhone 4s and an IPad 3 ... all running IOS 7.0.2. Same Exchange account on the same server.
If the 5s is flagging a message, the flag is only locally on the 5s, as all reporting here. The other IDevices can flag correctly and the flag is distributed immediately to the server and other devices.
But the 5s can UNFLAG a message, this is in this case distributed correctly to the server.
Reported it by phone to the Apple support ... will do the same ith the feedback above.
BTW: It's not only an Exchange problem but an ActiveSync problem. I'm running Kerio Connect with Active Sync in my environment.