If you have iron in the coils, you will get very strong preference positions in the clogging torque for the given number of poles and stator coils and this will certainly give starting problems. It is possible to make an axial flux generator with iron in the coils but then you need another ratio in between the number of poles and the number of coils. This ratio can be 10 : 9. This ratio is also used for hover board motors for which one uses 30 poles and 27 coils.
Assume that you use 10 poles and 9 coils. So the armature pole angle is 360 / 10 = 36° and the coil angle is 360 / 9 = 40°. If you have two iron armature disks with the magnets at the inside and the stator with coils in between, you need 20 magnets. You can best take circular magnets and circular coils. The coils of the three phase U, V and W have to be laid in the following sequence: U1, U2, U3, V1, V2, V3, W1, W2 and W3. Coils of the same phase are connected in series.
If the north pole N1 is just opposite coil U2, the south south poles S5 and S1 are almost opposite to coils U1 and U3 but there is an angle of 4° difference. But this is no problem as it results in a small positive phase angle of 20° in between the voltages generated in coil U2 and U1 and a small negative phase angle of -20° in between the voltages generated in coil U2 and U3. This small phase angle makes that the resulting voltage is only a little lower than if all three voltages would be exactly in phase. As a south pole is about opposite to coil U1 and U3 when a north pole is opposite to coil U2, coils U1 and U3 have to be wound left hand if coil U2 is wound right hand! It is easy to prove that there is a phase angle of 120° in between the voltages generated in coils U2, V2 and W2, so the given winding is a 3-phase winding. You need a 3-phase rectifier with six diodes to rectify the AC current.
For the given ratio 10 : 9, you will get 10 * 9 = 90 small preference positions per revolution, so a preference position every 4°. The advantage of using iron in the coils is that the air gap is much smaller than for a generator with no iron cores in the coils and therefore the generated voltage per turn will be a lot higher. The peak torque will also be a lot higher. However, if you use massive iron bar as core, you will get eddy currents in the iron and these eddy currents make that the cores will become warm and that you need an extra torque for these iron losses. Dissipation of the heat generated in the cores and in the coils is difficult as the cores and coils are enclosed by the armature disks. So the peak efficiency might be lower than for a stator with no iron in the coils. But it might work if you limit the maximum rotational speed.
If your generator isn't big enough for 10 poles and 9 coils, you can also use 20 poles and 18 coils but in this case the coil sequence becomes U1, U2, U3, V1, V2, V3, W1, W2, W3, U4, U5, U6, V4, V5, V6, W4, W5 and W6. In this case you have the option to connect a coil bundle of three coils in series to the other coil bundle of three coils of the same phase for a high voltage and a low current or to connect them in parallel for a low voltage and high current.