To my knowledge, there is no such effort being done.
The two languages seem to have similar capabilities, so I'm not sure why this wouldn't be possible.
Is it possible ? Probably. Both Dart and Nim can target Javascript so you can probably bridge the two. But you'd also have to wrap the entirety of Flutter libraries & widgets in order to use them from Nim and that would be a huge tasks.
IMO either you :
OR
Flutter is a big stack, which includes both C/C++ ("the engine") and a Dart framework ("the framework").
https://flutter.dev/docs/resources/architectural-overview
Trying to recreate either the engine or the framework alone is a massive undertaking. Reusing the engine seems like a viable approach, given Nim's great C/C++ interop. Reusing the framework seems more challenging, although a "transpilation" approach from Nim to Dart seems viable as well (similar to Nim -> JS as others have pointed out).
tanslating dart to nim so that nim only could be used
I don't think so. How do you transpile a class-based, object-oriented language to one that's not? Implementing a Dart backend for Nim would be more realistic, as a Nim object type could be mapped to a Dart class.
Flet looks interesting. I actually wrote some code for my own approach, named DocUI. It works similarly, and you could write the code to run on the server using Nim or even other languages too. However's was no front-end scripting support, which is a problem Flet could hit as well. This means its difficult to build reactive UIs where one component immediately reacts to another component's state. It's not unsolvable, but not pleasant to implement either. I'm still trying to decide what to do with DocUI, I may just upload it to GitHub and leave it at that.
I've also being building a project with Next.js/React, and I've been trying to see where Nim could fit into the picture. With Status's GraphQL implementation (https://github.com/status-im/nim-graphql), it should be possible to write React code on the front-end with Nim on the server-side, answering REST and GraphQL requests. But I haven't tried to implement anything like that yet.