As FaunaDB documentation, it seems that there is no dart API nor REST API. Also, I can't find the FaunaDB package in the Flutter Packages.
Is there any way to use the FaunaDB on the flutter?
Currently we don't offer first party support for flutter. You can build a third-party driver for Dart based on our current open source drivers if you'd like. They do use json/http under the hood. If you are targeting android another option might be to fork the java driver and switch out http clients to be android friendly and use a platform channel.