1974 I was a student on 3 Sqn at No 4FTS Valley flying the Hunter. We had just started the formation phase when I was confronted by a similar incident.
By no means do I claim that what happened was correct but sometimes luck does play a part in the outcome.
We were Number 3 flying in Vic formation in a Hunter T7. As student I was flying in the left hand seat with my QFI in the right. He was demonstrating a formation approach and overshoot (go round in modern terms). As we were on the left of the formation I had to look across my QFI and so the picture was more difficult to assimilate. There was a lot of movement of the flight controls and rapid throttle inputs. All went well until the overshoot. Just after the gear was retracted we started to drop back. I glanced at my QFI and then to the engine gauges. Rpm decreasing (despite my QFI having full throttle selected) and decreasing JPT - Flame Out.
As my QFI lowered the nose I selected the Relight ON (only available to the pilot in the left seat) and watched. We were pointing directly at the 18th at the Rhosniegr Golf Course, 180kts and descending through xxxft. Almost immediately the engine relit and the JPT rose. My QFI mutter something which I cannot recall apart from "Arr, its OK now" as the engine wound up through 7000 rpm.
It was only after the incident the I realised that we had MAYBE pressed on to a position that was outside the seat limits. On reflection we should have ejected at 180kts/200ft.
There is no doubt that the first indication of the flame out was the lack of thrust causing us to drop back. This should have been more obvious to the flying! The second indication was the gauges. Although only a student I had it hammered into me how to recognise flame outs, surges/stalls and mechanical failures and their differences. Indeed, it was not unknown for any of these to occur on both the JP and the Hunter if flown aggressively. I agree that Capt Casey was not trained to be able to assimilate this kind of information. Her brief would have been to do as told by her pilot.