It is a (rather poor) representation of the Canadian Forces School of Administration and Logistics (CFSAL) badge. The first attached image (taken from a pdf document from CFSAL) is what the full badge should look like. It appears CFSAL has been renamed the Canadian Forces Logistics Training Centre (CFLTC) and has a new badge (second attached image) according to the
Canadian Register of Arms, Flags and Badges
As for official wear (if any) of the badge, I can only make a guess. I was never posted to CFSAL, nor to any other of the schools on CFB Borden, but I did a couple of courses at CFSAL even though I was neither Admin nor Log branch. I faintly recollect staff (not students) at some of the schools wearing embroidered school badges on the right breast (above the pocket and name tag) of the "work dress" jacket. Work dress was a uniform worn during the period (following unification) when all elements of the Canadian Forces wore the same green uniforms. We went back to wearing separate uniforms in the later 1980s. After a quick look through some old course photos, I did come across one picture (from 1985 or 86) showing an officer wearing work dress jacket with a school badge (CFMSS) in the location I previously noted. I don't know if the badge you showed was used for this purpose, but regardless it would not have been worn on any form of headdress.
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