General aviation instructor pilot reported a near miss with a military trainer at a non-towered airport in VMC conditions during a training flight. The instructor pilot reported the military trainer performing non-standard military operations at the public use airport creating a safety hazard; resulting in the near miss with the instructor pilot.

Narrative

Prior to DINGS (FAF) we announced 10NM straight-in and commencement of the VOR/DME-10 approach into GZH; low approach only. This was a routine instrument training ride under Part 91. Once in a stabilized descent inbound the field ~ 1800 [ft.] MSL a military [Aircraft Y] suddenly appeared extremely close on my ADS-B; easily within a few hundred feet laterally; 300 ft. below. I as the instructor/safety pilot directed my student to level off; proceed on course while I tried to determine the intent of [Aircraft Y] at my rear over CTAF. Looking back I could see the aircraft in a hard left turn diverging away from me and [Aircraft Y] announced a variety of non-standard military jargon over CTAF (i.e. '360s'; 'break'; 'initial'; 'report 3 mile final'). Unclear of his intent; we self-announced our decision to terminate the approach; climb to south and proceed back to Pensacola. [Aircraft Y] callsign is attached to [location]. I'm extremely tired of this organization's non-standard military operations and conduct at public use airports. Their disregard for AC 90-66C - Non-Towered Airport Flight Operations - is a safety hazard.