Did you read the bit where it says :- 96 KBytes of SRAM
That means that the Due as most ram than most Arduino have flash / eeprom / sram put together.
o.k 96k of ram , 5 seconds , 4 sensors
4 sensors at 32 bits each ( 4 bytes ) 4 * 4 = 16 byte
96k and say 80k usable ? ( 80 * 1024 ) / 16 = 5120 * 5 seconds = 25600 seconds of 4 sensor data.
25600 / 60 / 60 about 7 hours of data , without storing it , And you can double that for you only need 16 bit per cell .
Yea, I know the arduino due got not a lot of ram, but I am not sure if storing in the flash is a good idea. Maybe you can better get an external memory chip the sam3x can interface natively. (Look in the datasheet)