Is there a way I can run a python Script when a button programmed in flutter is pressed?
I know it's quite old now but may be someone else can get help out of it. There is library called starflut and it can incorporate python code inside your flutter app. Take a look here
If you want to use pip packages with a python script, I suggest you, chaquopy package, as it allows you to use the majority of text-based pip packages.