What type of transistor generally has the lowest flicker noise?
It depends on the crystalline structure of the epitaxial wafer and junction geometry and square of the current needed for bias in both conductor and dielectric.  Flicker Noise is random pink noise usually measured &lt;100Hz in \$A^2/Hz \$ as 1/f noise, but contributes to phase noise in RF.


GaAs can be much better or worse than Si.
carbon resistors are worse than metal film which are worse than copper resistors which are worse than  "NP0" manganin conductors considered flicker noise-free.


The explanation is simple but hard to visualize.

Imagine a small low leakage  cap on a unijunction gate or a DIAC with a small bias current and a breakdown voltage for the semiconductor shorting out the cap and then charging up again. This is a fixed f relaxation oscillator.  Now imagine that certain semiconductor crystals have a higher leakage current (Early Effect) with greater BDV generating bigger partial discharges between charged molecules before they break down under the electric field (in a nano scale ) . Then imagine millions of relaxation oscillators of random pulse rate low pass filtered by the dielectric between the charged conductor atoms.  So this RC time contant affects the relaxation rate while the high series leakage and shunt capacitance low pass filters these broadband pulses or "flickers".

So in my theory, it is the device with the highest RC leakage time constant and highest BDV where the product produces a corner frequency at some A^2/Hz with applied bias voltage.  I call this flicker, random (PD) or partial (nano crystalline) discharge , for your understanding and consideration.

Which device?. depends on conduction power, leakage input bias current, dielectric doping levels, crystalline épiwafer nano-structure and meta structure such as FET, BJT or HJT.

But we know for sure how to rank conductors as I did above so we generally use MF for lower noise exclusively and carbon or WW where high current noise does not matter.

I don't know how to tell you which device has lowest random flicker noise for ANY random design.

... but you may look at GaAs FETs and compare.