I have a working system on 0.13.1+1. Upgraded to 0.14.0 and made relevant changes to getIdToken:
FirebaseUser user = await FirebaseAuth.instance.currentUser();
String idToken = await user.getIdToken();
became
FirebaseUser user = await FirebaseAuth.instance.currentUser();
IdTokenResult idTokenResult = await user.getIdToken();
String idToken = idTokenResult.token;

However, I now get a failure which closes the app instantly
java.lang.IllegalArgumentException: Unsupported value: null
at io.flutter.plugin.common.StandardMessageCodec.writeValue(StandardMessageCodec.java:294)
at io.flutter.plugin.common.StandardMessageCodec.writeValue(StandardMessageCodec.java:291)
at io.flutter.plugin.common.StandardMessageCodec.writeValue(StandardMessageCodec.java:291)
at io.flutter.plugin.common.StandardMethodCodec.encodeSuccessEnvelope(StandardMethodCodec.java:57)
at io.flutter.plugin.common.MethodChannel$IncomingMethodCallHandler$1.success(MethodChannel.java:225)
at io.flutter.plugins.firebaseauth.FirebaseAuthPlugin$2.onComplete(FirebaseAuthPlugin.java:554)
at com.google.android.gms.tasks.zzj.run(Unknown Source:4)
at android.os.Handler.handleCallback(Handler.java:790)
at android.os.Handler.dispatchMessage(Handler.java:99)
at android.os.Looper.loop(Looper.java:164)
at android.app.ActivityThread.main(ActivityThread.java:7000)
at java.lang.reflect.Method.invoke(Native Method)
at com.android.internal.os.RuntimeInit$MethodAndArgsCaller.run(RuntimeInit.java:441)
at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:1408)