What are the major causes of flameout, excluding ingestion of foreign objects?
You might be counting this as FOD, but I'm going to go with water.  That is, more rain volume than the engine can handle.  It's the reason you select continuous ignition while in moderate to heavy rain because the chance of flameout is quite high.

Next in line would be flow disturbances at very high altitude, that are normally tolerable at low altitude.  Airliners that have gotten into high altitude stall incidents can flame out one or more, especially airplanes with tail mounted engines that are in the wing's down wash.  

On some airplanes the stall protection system will activate continuous ignition automatically when you are close to or at stick shaker.  Modern FADEC engines usually have an auto-relight function built in and have to demonstrate auto-relight capability for certification.

Fighters like the 262 and other first generation engines had a fuel control system that was basically a needle valve connected to the thrust lever. The pilot's eyes and brain was the real fuel control and the gauges had to be monitored carefully when making power changes.

In the early 50s hydro pneumatic fuel controllers allowed "slam acceleration" without flaming out, but engines were still sensitive to flow disruptions.  Then  variable guide vanes came along to manage the flow through the axial compressor to control blade angle of attack, and flame outs due to flow disruptions only occurred with more extreme conditions.