Is it possible to build android widgets in flutter?

As the OP mentioned in an edit, this isn't currently possible because Flutter uses a custom rendering engine.

Widgets are quite limited in what they can render; the documentation explains that only certain layouts may be used. You could theoretically use Flutter's software renderer to render to an image in a seperate instance from the main one and display that, but that would be very technical, likely not very performant, and not straightforward at all!

Here is a quite detailed tutorial for widgets that guides you through creating a few examples although in Java. The same logic applies with just a few syntactical changes for Kotlin as the classes are pretty much interchangeable. However, realistically, most of the work is in the layout with some wiring in android; if you're already familiar with Android & Java, keep in mind that Kotlin does add a bit to your app size (The Kotlin runtime adds about 7,000 methods and ~1MB to your debug APK from the kotlin on android FAQ) and since most of your logic should be in flutter you probably won't have all that much Kotlin/Java code if this is all you're using it for (although if you're new to both Java & Kotlin, Kotlin is arguably more friendly in some ways).

Also, to be able to communicate between your flutter app and the java/kotlin backend, you'll need to use platform channels as described in the flutter documentation.