If I save information in the flash memory, when I switch off the arduino board, will I loose that information?
No, you won't. But getting data into the flash memory is difficult. Perhaps you can use EEPROM memory? See https://www.arduino.cc/en/Tutorial/Memory
Writing to flash also works but requires 'tweaked' bootloader. See Writing to FLASH from application. Please test and enjoy :-) - Microcontrollers - Arduino Forum