Just had a go at this and it’s easier than you might expect.
First, create a folder that lives in the same directory than your tests are. For example, I created a folder called test_resources.

Then, let’s say we have the following JSON file for testing purposes.
test_resources/contacts.json
{
"contacts": [
{
"id": 1,
"name": "Seth Ladd"
},
{
"id": 2,
"name": "Eric Seidel"
}
]
}
test/load_file_test.dart
We could use it for our test like so:
import 'dart:convert';
import 'dart:io';
import 'package:flutter_test/flutter_test.dart';
void main() {
test('Load a file', () async {
final file = new File('test_resources/contacts.json');
final json = jsonDecode(await file.readAsString());
final contacts = json['contacts'];
final seth = contacts.first;
expect(seth['id'], 1);
expect(seth['name'], 'Seth Ladd');
final eric = contacts.last;
expect(eric['id'], 2);
expect(eric['name'], 'Eric Seidel');
});
}