How to change the entire theme's text color in Flutter?

I think TextTheme.apply is what you want. bodyColor will be applied to headline, title, subhead, button, body1, and body2. displayColor will be applied to display1 through display4, and caption. If you specify both bodyColor and displayColor and use the same color value, that will effectively change text colors on all text styles.

Example:

final newTextTheme = Theme.of(context).textTheme.apply(
  bodyColor: Colors.pink,
  displayColor: Colors.pink,
);

To provide an alternative that seems to work without setting all the Text styles directly is to change the style of the DefaultTextStyle at the place in the Widget tree to take effect

return DefaultTextStyle(
  style: TextStyle(color: Colors.pink),
  child: _YOUR_WIDGETS_
)

For the entire app, you can set textTheme property in the Material app widget.

MaterialApp(
  theme: ThemeData(
    textTheme: TextTheme(
      bodyText1: TextStyle(),
      bodyText2: TextStyle(),
    ).apply(
      bodyColor: Colors.orange, 
      displayColor: Colors.blue, 
    ),
  ),
)