You can write software for Fuchsia without using Flutter, but Flutter is the most friendly way at present.
In a basic sense, Flutter is based in Dart, but if you want to call into another language like Swift, there is a way to do so, called FIDL. I'm not sure if Swift has FIDL bindings yet, but I'm sure that it and many other languages will, in time.
Even today Flutter has support for Swift code on iOS the same way it supports ObjC, via MethodChannels. (This is also true for Java and Kotlin code on Android.)
I'm not terribly familiar with the landscape, but my suggestion is broadly applicable: learn both.
A developer shouldn't be constrained to a single language. Pick the one that's suitable for the project you want to work on. For the next project, do the same. In my experience you'll find it progressively easier to pick up new languages (and stacks, and paradigms, etc.) each time you do it.
IMO, a developer's goal should be to understand and implement design patterns, not individual languages.
... and for the record, I say this as someone who prefers a single language (Python) to all others I've encountered.
Fuschia is getting swift support Flutter runs on fuschia Flutter uses dart
Do I learn dart or swift, personally I want to learn swift. Flutter only supports dart??? Fuschia supports swift
Is flutter going to support swift