It appears that the best way to try to get a death certificate will be to contact the Ministry of Home Affairs at Lusaka, Zambia. The FamilySearch Wiki article titled Zambia Civil Registration at https://www.familysearch.org/wiki/en/Zambia_Civil_Registration has some details about civil registration in Zambia that you may find useful.

I've often been told that the first step we should take in tracing an ancestor is to "Kill them off" so looking for the death certificate for your father's uncle makes sense. Depending on what you are trying to learn the search for this death certificate may not be very productive especially since deaths were not commonly registered until the last year or two.