This is a code for an auth interceptor for Dio, which uses a header to avoid retrying indefinitely to refresh the token.

auth_interceptor.dart

/// This interceptor is simplified because is doesn't contemplate
/// a refresh token, which you should take care of.

/// I haven't tested this code, but I believe it should work.
/// If you have some feedback, please leave a comment and I'll review it :) Thanks.

class AuthInterceptor extends InterceptorsWrapper {
  final Dio loggedDio;
  final Dio tokenDio;
  final SomeLocalStorage localStorage;

  AuthInterceptor({this.loggedDio, this.tokenDio});

  @override
  Future onRequest(RequestOptions options) async {
    /// access token obtained via API after user logged in and saved into 
    /// some local storage
    final accessToken = localStorage.getAccessToken(); 
    options.headers['Authorization'] = accessToken;
    return options;
  }

  @override
  Future onError(DioError error) async {
    if (e.response?.statusCode == 401) {
      //This retries the request if the token was updated later on
      RequestOptions options = error.response.request;
      if (options.headers['Authorization'] != localStorage.getAccessToken()) {
        return loggedDio.request(options.path, options: options);
      } else {
        _lockDio();
        if (options.headers['Retry-Count'] == 1) {
          _unlockDio();
          // Here you might want to logout the user
          return error;
        }
        return tokenDio.get("/token").then((response) {
          localStorage.setAccessToken(response.data['data']['token']);
        }).whenComplete(() {
          _unlockDio();
        }).then((e) {  
          options.headers['Retry-Count'] = 1;
          return loggedDio.request(options.path, options: options);
        }).catchError((e) {
          // Here you might want to logout the user
          return e;
        });
      }
    } else {
      return error;
    }
  }

  void _retryRequest() {

  }

  void _lockDio() {
    loggedDio.lock();
    loggedDio.interceptors.responseLock.lock();
    loggedDio.interceptors.errorLock.lock();
  }

  void _unlockDio() {
    loggedDio.unlock();
    loggedDio.interceptors.responseLock.unlock();
    loggedDio.interceptors.errorLock.unlock();
  }
}