Look at U8 on the schematic. /WP is 3.3V i.e. you can write to the Flash chip.
Follow the SCLK line. CLK on U8. Into B1 on U2. Out of A1 on U2. Select J5 to route it to your Arduino JP5 (ICSP header).
Do the same for FLASH_CS, SDO, SDI on U8.
I am sure that the Manual gives you instructions.
Mount the Flash chip. Make/break the relevant solder-bridges. The EastRising boards are very well designed.
Then test the Flash chip with examples from the third party Arduino library e.g. for W25Q128FVSSIG
Personally, I would test the microSD first. i.e configure the correct solder-bridges. Run examples from the official <SD.h> library.
When the microSD is working, I would try the Flash chip.
I do not own your screen or your Adapter.
I do have an EastRising Adapter for RA8875. I do own a Flash chip.
If you have a problem, I can mount the Flash chip on my Adapter board i.e. follow my own advice and walk you through the steps.
David.