AT APRX 1331 CDT, THE PLT ENTERED THE PINE BLUFF FSS STATION & REQUESTED A BRIEFING FOR A VFR FLT TO SPRINGFIELD, MO. HE WAS ADVISED THAT VFR FLT WAS NOT RECOMMENDED. THE PLT RETURNED AGAIN BETWEEN 1335 & 1350 & WAS SEEN EXAMINING THE WX CHARTS. AT APRX 1420, HE TOOK OFF WITHOUT FILING A FLT PLAN & REMAINED BELOW THE CLOUDS DURING DEPARTURE. A SHORT TIME LATER, THE ACFT WAS SEEN FLYING UP THE ARKANSAS RIVER AT LOW ALTITUDE WHERE POWER LINES CROSSED THE RIVER. THE PLT PULLED UP TO CLEAR THE POWER LINES. REPORTEDLY, HE PULLED UP, STALLED, THEN RECOVERED & TURNED AWAY FROM THE RIVER. MOMENTS LATER, IT RETURNED HEADING DOWN RIVER BACK TOWARD THE POWER LINES. REPORTEDLY, IT STALLED AGAIN, IMPACTED THE WATER & SANK. ALL 3 OCCUPANTS DROWNED. THERE WAS EVIDENCE THAT THE FRONT SEAT OCCUPANTS WERE NOT USING THEIR SEAT BELTS & SHOULDER HARNESSES & BOTH HAD RECEIVED TEMPORAL & FACIAL LACERATIONS.