Although Flame does not implements Box2d itself, it bundles a forked port of the Java Box2d to Dart by Google.
The source of the bundled box2d on Flame can be found here.
There is also a simple example game that can be used as reference of how to use box2d on Flame here.
If you are going to use Box2D in your project it can be a good idea to use the Box2D specific
extension of the BaseGame class. It is called Box2DGame and it will control the adding and
removal of Box2D's BodyComponents from your root Box2DComponent.
A simple Box2DGame implementation example can be seen in the examples folder.