[FlightRPC][Integration] Ensure all RPC methods are covered by integration testing

This would help catch issues like https://github.com/apache/arrow/issues/13853

**Reporter**: [David Li](https://issues.apache.org/jira/browse/ARROW-17568) / @lidavidm
#### Related issues:
- [[Flight] Test Flight servers and clients with a generic gRPC services](https://github.com/apache/arrow/issues/20981) (relates to)

_{**Note**: *This issue was originally created as [ARROW-17568](https://issues.apache.org/jira/browse/ARROW-17568). Please see the [migration documentation](https://github.com/apache/arrow/issues/14542) for further details.*}

Start by locating the existing FlightRPC integration tests and enumerating the RPC methods exposed by the Java implementation. Compare the two sets, then add coverage for methods that are missing; done means every RPC method is exercised by integration tests and issues like the linked Arrow 13853 case are detected.

Written by the indexing model from the issue text.