Air Zimbabwe are indeed extremely difficult to make bookings with or find out any information. Their website gives very little detail and they don't have an online booking system or online payment and card facilities.
Regarding their flight schedule: Harare to Victoria Falls Mon/Wed/Frid departing at 08.00 arriving VF at 09.00 Teus/Thurs depart at 09.30 and arrive VF at 10.30 Sat depart 07.00 and arrive at 09.00 Sun depart 10.00 and arrive at 12.00
Victoria Falls to Harare:
Mon/Wed/Frid departing at 16.30 arriving Harare at 17.10 Teus/Thurs depart at 11.00 and arrive Harare at 12.00 Sat depart 9.30 and arrive at 10.30 Sun depart 12.30 and arrive at 13.30
To my knowledge there is no agent who will book these for you. You can call Air Zimbabwe reservations on +263 4 575021 and book your flight but you will have to make some arrangement for the payment as these have to be paid to their offices in Harare or Victoria Falls.
These are this years schedule so I can't be sure of next years just yet.