The F-14 is special; to stop the flat spin you need to pull on the stick. Then the spin can be recovered from.
This is different from what you learn about regular spins, where pushing the stick would be a better recovery method. In a flat spin, the forward fuselage dominates the aerodynamic forces, and we all know there are no control surfaces which could influence this flow. Wings and horizontal surfaces are fully separated, and elevator deflection is mostly useless. As others have pointed out before, a flat spin can only be stopped by shifting the center of gravity forward or deploying a spin chute. The F-14 was an exception.
Spinning the F-14
Early on, the Navy lost several F-14s due to flat spins. They then studied the phenomenon at Pax River, and in the end Bill Bihrle found out that the elevator shields airflow from the two vertical tails of the F-14 when the stick is pushed, but moves out of the way when the stick is pulled full aft. You have to know that the elevator of the F-14 is a full-flying surface, and the movement range is from -20° to +70°. At +70° it is almost in line with the airflow in a flat spin, and now the vertical tails are no longer in the wake of the elevator. They now can reduce the high yaw rate, which in turn reduces the high pitch-up moment of the rotating fuselage. With the lower inertial pitch-up moment, the elevator then has to be moved back to neutral, and the drag from wing and elevator is enough to pitch the aircraft fully down and out of the spin.
Naturally stable flying wings never enter a flat spin; their spin modes are all fairly steep due to the lack of a strong inertial moment from the lengthwise distribution of masses.
Influence of mass distribution
I guess I now need to explain the inertial moment which causes the high pitch attitude in some aircraft. The axis of the spin rotation is close to the aircraft's nose, and the tail has the biggest distance from this axis. In a flat spin the axis of rotation is even more back, close to the center of gravity. All parts of the aircraft rotate with the same yaw rate, and the centrifugal force from this yawing motion grows linearly with distance from the spin axis. This difference in centrifugal force along the lengthwise coordinate of the aircraft pulls the aircraft in a near-horizontal attitude.
Watch this movie of the spinning XB-70 to get an idea how it looks. Depending on elevon settings, the spin axis is somewhere between the cockpit and the forward tip of the wing triangle. With the damaged configuration(watch without sound for no distraction) you get a typical flat spin with the spin axis close to the center of gravity since there are few suction forces acting on most surfaces - only drag and the nose vortex (more on that below) remain.
How to avoid flat spins
If you have a configuration which is prone to flat spins, you need to change the shape of the fuselage tip. A rotating fuselage tip at high angle of attack will produce vortices at its side, and the yawing moment of these vortices will grow stronger with increasing yawing motion. This is why a flat spin is self-stabilizing. One way to suppress these vortices is the placement of small spoiler strips along the nose (which fixes the vortex position and reduces this self-stabilizing effect), and another is to make the nose shape flatter.
Unfortunately, this can only be done long before take-off.
Answer to your question
Regarding the "Top Gun" scenario: If the F-14 is at high angle of attack and the jet wash hits it asymmetrically, the airplane could enter into a spin. But from there it is still some way to the fully developed flat spin, and I would expect that a skilled pilot could recover from this momentary upset.