Provided neither Nginx and Gunicorn are used, are the hardware specs of the Pico enough to handle a very simple flask app? Also, does the Pico's MicroPython support flask? If not, how can I simulate such behavior on the Pico?
No, even putting the severely under powered CPU and lack of dependency support aside, the 264KB of onboard ram is nowhere close to enough to run a flask server. Just importing flask into python takes over dozen megabytes of ram.
If you needed something very light and inexpensive to do this you would be much better off getting a Raspberry Pi Zero W.
I'm using an automation 2040w board
Have a look here.
This has allowed me to run code remotely from a url in browser or with python requests module