THE PLT REPORTED THAT ON THE PREVIOUS FLT, THE CENTER FUEL TANK GAUGE WAS MALFUNCTIONING AND INDICATED 800 LBS EVEN WHEN IT WAS FULL WITH 1400 LBS. AFTER LNDG AT CHARLOTTE,NC, IT WAS STILL INDICATING 800 LBS. BFR TKOF, THE CENTER TANK WAS REFILLED. WHILE EN ROUTE ABOUT 40 MI WEST OF ATLANTA, GA, THE PLT NOTED THAT THE FUEL GAUGE INDICATED 500 LBS & WAS DROPPING RAPIDLY. A FEW MINUTES LATER, BOTH ENGS FLAMED OUT. VECTORS WERE OBTAINED TO FLY TO THE NEAREST ARPT. DRG THE DESCENT, THE ENGINES WERE RESTARTED. THE PLT INTERCEPTED THE ILS & REMAINED HIGH ON THE GLIDE SLOPE. THE WEATHER AT THE ARPT WAS REPORTED AS 100 FT OVC, VIS 1/4 MI WITH FOG & RAIN. THE ACFT BROKE OUT OF THE CLDS APRX 2/3 OF THE WAY DOWN THE RWY, THEN CONTINUED OFF THE END OF THE RUNWAY & WENT THRU ILS ANTENNA ARRAY. AN EXAM REVEALED THE CENTER FUEL CAP WAS MISSING, IT WAS FOUND IN THE GRASS NEAR THE PARKING RAMP AT CHARLOTTE. THE FUEL CAP WAS FOUND TO BE WORN & WOULD NOT LOCK SECURELY.