Flutter padding for all widgets?

You can use Padding, which is a very simple Widget that just takes another Widget as a child and an EdgeInsets object like the one you are already using as padding.

This approach of "composition over inheritance" in Flutter is very intentional. You can find a recent discussion of the pros and cons on Flutter's Gitter channel.

Here is a supplemental answer that provides some code. As the accepted answer states, you can use the Padding widget. Flutter is different than Android or iOS because Padding is a widget rather than a property. (It is a property of Container, but internally it is still a widget.)

This is a Text widget wrapped with a Padding widget.

Padding(
  padding: const EdgeInsets.all(8.0),
  child: Text("text"),
);

See my fuller answer here.