[Flight] Add Client Infrastructure (#17234)

* Change demo to server

* Expose client in package.json

* Reorganize tests

We don't want unit tests but instead test how both server and clients work
together. So this merges server/client test files.

* Fill in the client implementation a bit

* Use new client in fixture

* Add Promise/Uint8Array to lint rule

I'll probably end up deleting these deps later but they're here for now.