I suggest that you use the microSD for storage. You can read and write files.
Yes, you can mount the Flash chip. Does it have the WP pin hard-wired? There should be a schematic.
If the WP is write-protected, you have to program the chip in a clamshell before mounting on the pcb.
It seems wiser to mount a Flash chip on the Adapter board.
And use the microSD socket on the display board. You can't access the microSD on the Adapter.
David.