What was found
TOOK OFF FROM KAUS AT 17:36 UTC. DURING CRUISE, AROUND 2 HRS AFTER DEPARTURE, FLYING AT FL 400, FUEL ON BOARD WAS 4500 LBS, VMC CONDITIONS, AND NO TURBULENCE, HEARD AN ABNORMAL NOISE FROM THE AFT SIDE OF THE PAX CABIN. SINCE NO ABNORMAL INDICATION WERE DISPLAYED IN CAS, CHECKED PRESSURIZATION SYS & WAS WITHIN NORMAL PARAMETERS. A FEW SECS LATER, HEARD A SIMILAR NOISE BUT THIS TIME THE RT ENG VIBRATED & PARAMETERS WERE FLUCTUATING, THE RT ENG FLAMED OUT. IDENTIFIED & CONFIRM THE RT ENG WAS FLAMED OUT, DECIDED TO DECLARE AN EMERGENCY & REQUESTED A LOWER ALTITUDE. TOOK CONTROLS AND COMMUNICATIONS AS PIC WHILE REQUESTING THE SIC TO PERFORM THE INFLT ENGINE FLAME OUT CHECK LIST. AFTER CHECKLIST PROCEDURE COMPLETED, MADE THE DECISION MAKING ASSESSMENT FOR ENGINE FLAME OUT FAILURE. AS A RESULT OF THE VIBRATION WE DID NOT ATTEMPT TO RESTART ENG. DURING DESCENT ATC SUGGESTED KFLG AS A POSSIBLE ALTERNATE AIRPORT, AFTER CHECKING PERFORMANCE, APPROACH PLATES, & WEATHER CONDITIONS, THE AIRPORT WAS SUITABLE TO LAND.