Flutter is not likely to be successful due to the amount of work required to maintain the UI compatibility, but if you are going to do shared UI then Flutter is the only one approaching it in a reasonable way IMO. Throw out the UI and _actually_ standardize on a unified system.
But yeah I don't think it will succeed in the long run.
Flutter is already the most popular cross-platform framework. React Native has more jobs at the moment, it has been around longer and JavaScript is popular.
However the reason Flutter is successful is because in a multi-platform world it let's you beat your competitors on cost, time to market and performance.
Dart is basically TypeScript or JavaScript with Flow, and with the exact same event loop concurrency model.
To say Flutter is the most popular cross-platform is naive. React Native is the most popular "mainstream" (aka HN) cross platform by a mile. Xamarin is huge especially within .net shops. Flutter is comparatively less mature and less adopted than either.
But yeah I don't think it will succeed in the long run.