App Flutter que no se conecta a Internet

Open the AndroidManifest.xml file located at <your_project>/android/app/src/main and add the following line:

<manifest xmlns:android="...">
  <uses-permission android:name="android.permission.INTERNET"/> <!-- Add this -->

From here:

Add the android.permission.INTERNET permission if your application code needs Internet access. The standard template does not include this tag but allows Internet access during development to enable communication between Flutter tools and a running app.

Another solution

Add these in Android Manifest file.

<uses-permission android:name="android.permission.INTERNET"/>

<uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"/>

Then run:

flutter clean
flutter pub get
flutter run