Projeto enviando com API. Foi um pouco confuso mas consegui.

import 'dart:convert';
import 'package:http/http.dart';

Future<void> sendProduct(Map<String, dynamic> product) async {
  
  String url = 'https://api.github.com/gists/33b84374a96cadc4e3aee103458e32fd';
  String chave = 'minha.chave.gist';
  
  Response response = await post(
    Uri.parse(url),
    headers: {
      'Authorization': 'Bearer $chave',
      'Content-Type': 'application/json'
    },
    body: json.encode({
      'description': 'descricao do gist',
      'public': true,
      'files': {
        'products.json': {
          'content': json.encode(product),
        }
      }
    }),
  );
  
  if (response.statusCode == 200) {
    print('produto enviado');
  } else {
    print('erro ao enviar produto ${response.statusCode}');
  }
}

void main() {
  var newProduct = {
    "id": 4,
    "name": "Monitor",
    "price": 800.00
  };
  sendProduct(newProduct);
}

// curl -L \
//   -X PATCH \
//   -H "Accept: application/vnd.github+json" \
//   -H "Authorization: Bearer <YOUR-TOKEN>" \
//   -H "X-GitHub-Api-Version: 2022-11-28" \
//   https://api.github.com/gists/GIST_ID \
//   -d '{"description":"An updated gist description","files":{"README.md":{"content":"Hello World from GitHub"}}}'