How to access the flash memory on the MKRMEM Shield

You can use the official "Arduino_MKRMEM" library.

Install it via the Arduino IDE's Library Manager (Sketch > Include Library > Manage Libraries). It comes with several example sketches that demonstrates its usage. You will find them under File > Examples > Arduino_MKRMEM in the Arduino IDE after you install the library.

You also have the option of using any other library or example code you find for the Winbond W25Q16DV flash chip the shield uses.