Is it possible to use Adafruit's Circuit Playground Express's 2MB storage in Arduino IDE?
In their guided tour of the Adafruit Circuit Playground Express, it specifically states:

You can use this in Arduino or CircuitPython to store files.

So yes, it is possible. As far as the how, according to this guide (also from Adafruit), that they have also made a library, Adafruit SPI Flash, which has a bunch of examples showing how to read from, write to, and format the SPI flash whilst retaining compatibility with CircuitPython, among other things.