I’m on a Linux system at the moment, so I can’t speak to “feel”. But in terms of “look” it doesn’t look any more native than electron does to me, just from these particular screenshots. I might even say it looks less “native” than wxWidgets, to me.
Flutter is extremely lightweight compared to Electron, and Dart is much nicer than vanilla JS. But the best part about it is not dealing with the DOM, which is absolutely terrible for UI development.
They look pretty native to me? What looks non-native? It’s certainly more native-looking than most Electron apps I’ve seen… Those tend to take the web approach of inventing their own standards for buttons/modals/etc rather than respecting the platform’s. (Not that that’s always bad! But it usually feels non-native.)
My relatively meager Dart experience is that it’s nicer to use than C++ and JS, but less nice than TypeScript. YMMV depending on your preferences.
The source list on the Mac version really stands out like a sore thumb to me. I’d have been almost certain it was electron had I seen the shot out of context.
Getting the native utility dialogs (file chooser, color picker, etc.) is probably worth it alone if Flutter does that, to be fair, if the cross platform build story is good and Dart is nice to use.
The look is only half of the game though. I’ve never seen a cross platform UI toolkit behaving natively, and integrating with the rest of the DE. Some paradigms are just too different.