DURING CLIMBOUT FROM MIAMI, A CABIN PRESSURIZATION PROBLEM WAS ENCOUNTERED. ALL CREW MEMBERS DONNED THEIR OXYGEN MASKS & THE CABIN ALTITUDE STABILIZED AT 20,000 FT AS THE ACFT WAS LEVELED AT 33,000 FT. ABOUT 40 MINUTES FROM DESTINATION THE FLIGHT ENGINEER TRAINEE/OBSERVER QUERIED THE FIRST OFFICER AS TO HOW MUCH LONGER THE FLIGHT WOULD TAKE. MOMENTS LATER THE TRAINEE STARTED TO SLUMP DOWN. THE FLIGHT ENGINEER TRADED MASKS WITH HIM AND VERIFIED THAT THE OXYGEN SUPPLY WAS NORMAL. AN EMERGENCY DESCENT WAS MADE TO 6,000 FT WHILE FIRST AID WAS ADMINISTERED. AN AMBULANCE MET THE FLIGHT AT THE DESTINATION & TRANSPORTED THE TRAINEE TO A HOSPITAL WHERE HE EXPIRED LATER IN THE DAY. CAUSE OF DEATH WAS LATER DIAGNOSED AS AEROEMBOLISM (BY EXCLUSION). THE TRAINEE HAD A CLINICAL HISTORY OF SEIZURES & LOSS OF CONSCIOUSNESS FOLLOWING DECOMPRESSION. THE PRESSURIZATION PROBLEM WAS REPORTEDLY RELATED TO A STUCK OUTFLOW VALVE.