There is already a package that fulfills all your needs, it is the StaggeredGridView.
It is not exactly the syntax you described, but the functionality should be greater or the same. You can add the gutters by setting mainAxisSpacing and crossAxisSpacing, set the column (or row, depending on the orientation) count by using crossAxisCount.
To specify the space which is used by the child, you define a staggeredTiles list, in which each StaggeredTile represents the child of the same index.
It is not exactly the same as the Bootstrap grid, but it comes close enough.
I've put together a super slim example:

import 'package:flutter/material.dart';
import 'package:flutter_staggered_grid_view/flutter_staggered_grid_view.dart';
void main() => runApp(MyApp());
class MyApp extends StatelessWidget {
@override
Widget build(BuildContext context) {
return MaterialApp(
home: Scaffold(
body: StaggeredGridView.count(
mainAxisSpacing: 8.0,
crossAxisSpacing: 8.0,
crossAxisCount: 12,
staggeredTiles: [
StaggeredTile.count(6, 6),
StaggeredTile.count(4, 1),
StaggeredTile.count(2, 2),
StaggeredTile.count(2, 2),
],
children: <Widget>[
Container(
color: Colors.red,
child: Text('6,6')
),
Container(
color: Colors.green,
child: Text('4,1')
),
Container(
color: Colors.blue,
child: Text('2,2')
),
Container(
color: Colors.yellow,
child: Text('2,2')
),
],
),
),
);
}
}