Axial flux PM-generators normally have a 3-phase, 1-layer winding. Such a winding is given in figure 5 of my report KD 341 for an 8-pole generator. In the upper picture, the legs of the coil bundles are laid on the ideal positions. This means that there is an angle of 15° in between the legs of adjacent coils of different phase and an angle of 45° in between the two legs of one coil. So within one coil, there are two positions which are not used. These positions can be used for a second layer with also six coils, so with also two coils of each phase. But this second layer doesn't make the winding a 6-phase winding. It is still a 3-phase winding as the coil laid in the grooves at 90° and 135° is the third coil of phase U and the coil laid in the grooves at 270° and 315° is the fourth coil of phase U. So you can get much more copper in a 2-layers winding than in a 1-layer winding. However, the amount of copper in a 1-layer winding can also be increased if the winding is modified such as given in the lower picture of figure 5. A disadvantage of using a 2-layers winding is that now you get crossing coil heads and this makes the winding thicker. It is possible to realise that the thicker coil heads are lying outside the path of the magnets and this is done for certain Chinese commercial generators. But a 2-layer winding is mostly too complex for non professional manufacture.
A 2-layers winding as described above, results in a 3-phase winding if all twelve coils have the same winding direction. However, if the six coils of the first layer are wound right hand and if the six coils of the second layer are wound left hand, the winding becomes a 6-phase winding. This is because change of the winding direction results in a 180° phase shift. Assume that the three phases of the first layer are called U, V and W and that the three phases of the second layer are called X, Y and Z. The sequence of the phases is now U, Z, V, X, W and Y and the phase angle in between adjacent phases is 60°. The three phases of each layer need their own 3-phase rectifier and both rectifiers must be connected in series. A 6-phase winding may have an advantage if the generated AC voltage isn't sinusoidal but if each AC voltage has a block shape with a rather large distance in between the blocks.
I have investigated a 5-phase and a 9-phase winding in my public report KD 712 for a radial flux PM-generator. A 9-phase winding (with a phase angle of 40° in between the phases) has as advantage that there is almost no fluctuation of the rectified voltage and current. Another advantage of a 9-phase winding is that it can be laid in a stator with 36 slots. A 6-phase winding (with a phase angle of 60° in between the phases) has no advantage above a 3-phase winding because a 6-phase winding has the same fluctuation of the voltage as a 3-phase winding if the voltage varies sinusoidal. This is because there is a peak in the DC voltage every 60° for a 3-phase winding (see report KD 340 figure 9).