[Full disclosure — I’m on the Flutter team.]
As Andrea says, and other people have responded, the general trend in mobile apps is toward design consistency across platforms. Or more significantly, companies are more concerned about their own branding than matching the brands of iOS and Android. As evidence of this, if you look at the most popular mobile apps (and apps that win awards) over the last few years, the look and feel is almost entirely consistent across the two platforms.
But it is also important to point out that other people (like you) are more concerned about taking full advantage of each platform. I personally think this is a temporary situation (e.g., most good webapps now use their own custom widgets, not the widgets supplied by each browser platform) but that doesn’t mean we can ignore the platform look and feel. In particular, apps need to utilize the affordances that users already know.
I compare this to the situation with automobiles. Here, the affordances are the steering wheel, accelerator, brake pedal, turn signal, etc. Of course they are extremely similar across many different brands of car. Nobody would be happy if a company decided to put the accelerator under the driver’s left foot (in early horseless carriages, differences like this were common). But other than the standard affordances, automobiles look and feel very differently across brands (and also very different across types of motorized vehicles, like sports cars, trucks, minivans, etc.).
And so it is with Flutter. The Flutter team spent a huge amount of time and effort to make things like scrolling look and feel as close as possible to each platform. Ironically, the hardest problem with doing this is that the affordances often change slightly between releases of iOS or Android (and for Android, sometimes between device manufacturers).
Because Flutter uses its own widgets, your Flutter iOS app will always look and feel like the latest version of iOS, even on an older version of iOS running on an older phone. And with the same codebase, your Flutter Android app will look and feel like the latest version of Android.
If you really do want to build a Flutter app that precisely matches the look and feel of a platform app to the smallest detail, Flutter gives the developer full control over every pixel on the screen. You can, if you want, make a Flutter iOS app look exactly (down to the pixel and how the animations work) the same as it would if it were written using Xcode and Swift or Objective-C. It is up to you.
Of course, there are still a few times when it will be better to use the platform tools to build a mobile app. I discuss those cases in this article: “Pitching Flutter to your company or client”.
Finally, you may have noticed that interactive screens are starting to pop up in more and more places, including smart TVs, home assistants, modern automobiles, home appliances, watches, and more. Flutter was designed to work on all of these platforms, not just mobile phones. The article linked in the last paragraph talks about how people have already ported Flutter to many of these platforms. And at Flutter Live!, Google demonstrated ports of Flutter than target desktop and notebook computers (Linux, macOS, and Windows), and standard web browsers. The world of smart devices is becoming far larger than just mobile phones, and Flutter will be ready.