is the flyback diode still required?
It might still be required.
From comments you said that the fan took 150 mA and, because a fan has some inductance, when the MOSFET deactivates you will see a peak voltage at the MOSFET drain of 150 mA × 100 Ω = 15 volts. That is 3 volts higher than the positive supply rail (12 volts). If the diode were present than it will clamp the back-emf to around 12.7 volts.
But because we are dealing with such low voltages it doesn't really matter. A 20 volt rated MOSFET would be adequate for both scenarios but, if your snubber resistance were (say) 150 Ω then, the peak voltage seen at the MOSFET drain would be 22.5 volts and exceed the MOSFET voltage rating.
If the fan took an amp whilst running up to speed and, the MOSFET deactivated during that period then, the peak voltage across the 100 Ω snubber resistor would be 100 volts.
So, it's down to the fine details as to whether you need a diode or not. You might need both because the snubber does slow ringing down and may reduce the EMI produced.