how to change icon color immediately after pressed in flutter?

You can simply put a condition for each color :

color:(isPressed) ? Color(0xff007397)
                        : Color(0xff9A9A9A))

and in the onPressed function :

 onPressed: ()
                      {
                        setState(()
                        {
                          isPressed= true;
                        });                    
                      }

You need to use setState() function. Wherever you are updating your variable values.

For example, I want to update my _newVar value to newValue and this should be updated into the view then instead of writing

_newVar = newValue;

it should be:

setState(() {
 _newVar = newValue;
});