L39 Pilot reported a drop an engine flame out during cruise. Pilot attempted unsuccessfully to restart the engine; then returned to departure airport and landed.

Narrative

Engine rollback occurred during confidence hop on Aircraft X; Day 0. Last flight was several months before. Fuel Controller replaced since last flight. Start; taxi and takeoff was normal. 'Engine Test (First Flight of the Day)' was performed twice with no issues noted. Flight consisted of a climb to 5;500 feet MSL to get away from the training aircraft and orbited just South of ZZZ Class D. Throttle was exercised through the full range while carefully monitoring engine response. No issues noted. Aircraft was flown West of ZZZ to a range of approximately 10-14 miles for UHF checks; still at 5;500 feet MSL. At this location and approximately 30 minutes of flight time the throttle was moved toward idle. The engine RPM dropped suddenly; and the 'GEN OFF' 'ENG OIL WARNING' lights came on. There may have been more; but these were the main ones that caught my attention. The situation was diagnosed as a flame out and the 'Immediate Air Start' procedure was applied but no engine response was achieved. Given the RPM was above 18% the 'Wind Milling Start' procedure was applied with reference to the checklist with no engine response. Closer examination noted the HPC RPM at approximately 25% and EGT around 250 Degrees C. Airspeed was held at 180 KIAS. Given the RPM; 'Alternate Air-Start Wind Milling (Emergency Fuel Circuit)' procedure was performed with reference to the checklist. Engine response was achieved and the throttle was set at a mid- range with enough thrust for level flight until a 'key' could be achieved for a straight in to [Runway] XXR. Landing was on XXR with approximately 15 knots of tailwind. The throttle was not moved until landing was assured. The engine remained running until shutdown. The aircraft was able to taxi clear on 'S' under own power. [Priority handling was requested] with ZZZ tower right offer the first air start attempt was unsuccessful. transponder code was entered. Crash; fire; rescue followed the jet to the FBO. Authorities took a picture of the aircraft tail number and my Pilot Certificate. I was informed no other report with ZZZ was needed.