As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
PILOT REPORTED ENGINE LT FLAMEOUT DURING CLIMB AT FL400. DESCENDED AND NORMAL RESTART AT FL220, RETURN TO DEPARTURE AIRPORT FOR MAINTENANCE. WILL UPDATE REPORT AFTER MAINTENANCE. MAINTENANCE COMPLIED WITH FLAMEOUT FLOW CHART FROM CJ610 MM SEI 186 FIG 101, NO DEFECTS NOTED.