What stops the magnetic field generated by the coil in series with the
MOSFET to induced a current in the coil in series with the diode
resulting in a simultaneous flow of current through the diode and the
MOSFET at the same time?
The dots on the windings on the transformer tell you that the voltage on the top of the primary is in phase with the voltage on the bottom of the secondary. This means that when the MOSFET conducts, there can be no current in the secondary because the secondary voltage produced will not be able force current backwards thru the diode: -
This is what happens in flyback designs during the energy charge part of the switching cycle. When charging is complete, the secondary flips polarity and drives current into the load and capacitor. The polarity flip is the flyback effect.
In reality there will be a little leakage current through the diode during the charge part of the cycle but nothing to alter the basic premise of this answer.