Yes, IMHO the world doesn't need another build system. Bazel sounds great, and the mobile development community seems to be converging arond it as the go-to tool for huge apps, e.g. see rules_xcodeproj [0].
It'd be a lot of work, because no good Bazel rules for Dart exist (there is [0] which is old and unmaintained, although it was recently forked [2] by a Google engineer working on Flutter), and of course, no rules for Flutter exist as well. Another problem here is that a lot of flutter_tools [3] code assumes that Android project uses Gradle, and iOS project uses Xcode.
After some investigation, it looks that to change this situation one could either:
(1) reimplement flutter_tools in Bazel, or
(2a) contribute to flutter_tools to work with Bazel, or
(2b) fork flutter_tools to work with Bazel (like you forked the engine)
Each of these is quite a lot of work. I'm curious to hear what you think about this.
[0]: https://github.com/MobileNativeFoundation/rules_xcodeproj
[1]: https://github.com/cbracken/rules_dart
[2]: https://github.com/matanlurey/rules_dart
[3]: https://github.com/flutter/flutter/tree/master/packages/flut...