How do I increment to the other bytes in the file being read?
What makes you think you are not getting all the bytes from the serial port? The fact that you write the value read from the serial port to every position in EEPROM does not tell you that you are not reading multiple bytes.
Remove the code that writes to EEPROM, for now. Just blink an LED each time there is data to read. See how many times the LED blinks.