THE STU PLT SAID THE ENGINE BEGAN TO ALTERNATE BETWEEN PARTIAL AND FULL POWER DURING THE INITIAL TKF CLIMB. THE ACFT WAS ABOUT 100 FT AGL AND ABOUT 300 FT PAST THE RWY END. ACCORDING TO THE STU THE INST TOOK CONTROL OF THE ACFT, TURNED LEFT, REVERSED COURSE AND HEADED TOWARD A TAXIWAY ON THE ARPT. THE TAXIWAY IS ORIENTED EAST-WEST AND IS EAST OF AND ALMOST PERPENDICULAR TO THE RWY USED FOR TKF, RWY 15. THE STU COULD NOT RECALL WHETHER THE ACFT LOST OR GAINED ALTITUDE DURING THE APPROACH TO THE RWY; HOWEVER HE SAID THE ACFT STAYED ABOVE THE ARPT. A WITNESS SAID HE HEARD ENGINE SOUNDS AS THE ACFT REVERSED COURSE. ACCORDING TO THE STU AS THEY NEARED THE TAXIWAY THE ACFT WAS STILL IN A LEFT TURN WHEN SUDDENLY IT STRUCK TREES ABOUT 200 FT SHORT OF THE EAST END OF THE TAXIWAY. A WITNESS SAID THE ACFT STALLED BEFORE IT STRUCK TREES. THE STU WAS RESCUED FROM THE ACFT BUT THE ACFT EXPLODED BEFORE THE INSTR COULD BE RESCUED. TWO RESCUERS WERE INJURED IN THE EXPLOSION. FIRE DAMAGE PRECLUDED DETERMINATION OF LOSS OF POWER. THE ACFT USED AUTO GAS.