[Java] Handle Flight Tests to gracefully shutdown.

### Describe the bug, including details regarding any error messages, version, and platform.

We have been experiencing a few flaky tests in Flight. And recently this was tracked in another PR https://github.com/apache/arrow/pull/43551#issuecomment-2328024081.

The root cause could be the issue discussed here. Shutting down the servers gracefully in order to release resources is necessary to avoid this flakiness in the tests.

### Component(s)

Java

Start by reviewing the flaky Flight test reports and the linked discussion in Apache Arrow PR 43551. Identify the Flight test servers that retain resources and determine how graceful shutdown should be coordinated. Done means the servers release resources reliably and the reported test flakiness is addressed.

Written by the indexing model from the issue text.