Don't understand the current direction in a flyback diode circuit
The loadspeaker is an inductor; so you have to create a good notion about its behavior. Here is a simple explanation.
Both capacitors and inductors are accumulating elements. They accumulate energy; so they can be considered as sources... rechargeable sources.
The capacitor can be thought of as a voltage source containing potential energy (as a tensioned spring). So, when discharges, it retains its polarity and passes a current in an opposite direction (the spring returns).
The inductor can be thought of as a current source containing kinetic energy (like an inert object). So, when discharges (step 4 in Fig. 2 below), it reverses its polarity and passes a current in the same direction (the object continues moving in the same direction).
You can investigate the inductor behavior by this attractive Flash movie. This is an exe file with embedded Flash player (it is absolutely safe since it is uploaded on my site of circuit-fantasia.com); so play and have fun. Here are two typical steps:

Fig. 1. The inductor is charging

Fig. 2. The inductor is discharging
Also, you can find an explanation of this clever circuit trick in another answer.