The authors of the posted paper are persistent with the idea that placing the oscillator active devices in Class C or even in Class D and F, the flicker noise of the oscillator will be improved by few dB's.
See papers: "An Ultra-Low Phase Noise Class-F2 CMOS Oscillator With 191 dBc/Hz FoM and Long-Term Reliability" and "A 1/f Noise Upconversion Reduction Technique for Voltage-Biased RF CMOS Oscillators".
First of all, experience teach me that never place the active device of an oscillator in other class than A or B, and avoid saturation of the active devices at all cost, because this will lower the loaded-Q of the resonator, since the device losses will then add to those of the resonator.
However, a reach in harmonics oscillator (as other classes than A and B has) will have a great influence in any type of phase noise measurements.
Flicker noise is dependent on the DC current through the active device.
The best option to minimize flicker noise is to use a high current device (big structure device, with high parasitic capacitance) biased at low current (usually 10x less then nominal).
Another option to reduce the flicker noise can be done through RF feedback. See U. Rohde papers and books about this topic.