If your problem is that the flutter build (APK, bundle) isn’t making API calls in a real device, this is because you need to add the Internet permission to Android Manifest before creating the release/build.
By default, “internet use” will work fine on the emulator but not on a real device.
To fix this, simply:
Open the file “android/app/src/main/AndroidManifest.xml” and add the proper user-permission:
<manifest>
...
<uses-permission android:name="android.permission.INTERNET"/>
...
</manifest>
And then create your build again.