Eistein said the instantaneous Brownian velocity is impossible to measure, he most likely meant that the time between collisions is so short, and the Brownian particle is so small to pin down among the surrounding fluid, that measuring it is technically impossible at his time.
If the movement discussed here can actually be observed (together with the laws relating to it that one would expect to find), then classical thermodynamics can no longer be looked upon as applicable with precision to bodies even of dimensions distinguishable in a microscope : an exact determination of actual atomic dimensions is #en possible.
I think what this means is the following. We know that thermodynamics is applicable to macroscopic systems, and we know that it is not applicable to individual molecules because thermodynamics laws arise as average statistical properties of many molecules. It does not make sense to apply thermodynamics to individual molecules. But what is the critical size for the applicability of thermodynamics? The fact that Brownian motion exists and can be observed under a microscope indicates that a micro-meter sized particle cannot be considered a macroscopic object, and thermodynamics should not be applied to such particles.
If Eistein thinks measurement of Brownian velocity is impossible, this quoted sentence is not where he expressed his opinion.