Question

Distinguish between ethyl chloride and benzyl chloride

Answer 1

Your observations are correct and on the short term, i.e. in the time scale of typical reactions in the lab, you'll hardly see an effect of the permanganate on chlorobenzene.

However, there seemingly have been attempts to decontaminate soil, e.g. on production sites, using permanganate for the complete oxidation of pollutants to carbon dioxide. But these processes are supposed to take much longer ( > 1 year) and usually don't play a role in considerations on what will happen under typical lab conditions.

But referring to the title, I'd rather suggest to simply record 1H1H NMR spectra of the compounds. Even on an ancient 90 MHz spectrometer, you'll be able to spot the signals of the benzylic protons at δδ = 4.5 ppm.