At what frequency does a non-polar molecule acquire a dipole able to participate in London Dispersion forces?
According to Prof. Loren Williams of Georgia Tech, the fluctuations occur on the femtosecond $\left(10^{-15}\ \mathrm{s}\right)$ time scale:


  
  
  Figure 13 shows how fluctuating dipoles of liquid Xenon (or Helium or Neon, etc) are coupled. Darker blue indicates higher electron density. The fluctuations are correlated and are very fast, on the femtosecond ($10^{-15}$ second) timescale. Adjacent Xenon atoms experience electrostatic attraction from the transient dipoles. Two different representations of fluctuating dipoles are shown.


This corresponds to a frequency of $1\ \mathrm{PHz}$ (petahertz), which is about five hundred thousand times faster than most modern computer processors.

Another estimate of the time scale (albeit one devised by me and thus of potentially suspect validity), is the SI value of the atomic unit for time, derived by dividing the reduced Planck constant by the atomic unit for energy, the Hartree (values are rounded a bit):

$$
\left\{atomic\ time\right\} = \frac{\hbar}{E_\mathrm{h}} = \frac{1.05457\times 10^{-34}\ \mathrm{J\cdot s}}{4.3597\times 10^{-18}\ \mathrm{J}} = 2.41888\times 10^{-17}\ \mathrm{s} \approx 0.024\ \mathrm{fs} = 24\ \mathrm{as}
$$

That last value is $24$ attoseconds, which is a well and truly short span of time. For comparison, this corresponds to a frequency of $41\ \mathrm{PHz}$.

Whatever the exact value, I have to believe the fluctuations are fast enough so as to be impossible to measure directly. (I would be fascinated to learn otherwise, though!)  Thus, even if different atoms/molecules do actually have different frequencies of London dipole oscillation, we have no way of finding out these values.