[Java][Flight] Flight SQL tests are flaky

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

Several test failures in `flight-sql` module have been observed in multiple job executions:
- https://github.com/apache/arrow/actions/runs/9185953424/job/25260768750
- https://github.com/apache/arrow/actions/runs/9185714602/job/25260156899?pr=41772

The reported issue is

```
Error: Errors:
Error: TestFlightSqlStreams.tearDown:224 » IllegalState Memory was leaked by query. Memory leaked: (250384)
Allocator(ROOT) 0/250384/250896/2147483647 (res/actual/peak/limit)
```

Note that there are also multiple messages about unclosed `ManagedChannels` in `flight-core` module:
- `org.apache.arrow.flight.auth2.TestBasicAuth2`
- `org.apache.arrow.flight.core/org.apache.arrow.flight.TestFlightGrpcUtils.testMultipleGrpcServices`
- `org.apache.arrow.flight.core/org.apache.arrow.flight.TestDoExchange.setUp`
- `org.apache.arrow.flight.core/org.apache.arrow.flight.TestServerOptions.addHealthCheckService`

```
May 22, 2024 5:50:41 AM io.grpc.internal.ManagedChannelOrphanWrapper$ManagedChannelReference cleanQueue
SEVERE: *~*~*~ Previous channel ManagedChannelImpl{logId=505, target=directaddress:///localhost/127.0.0.1:5555} was garbage collected without being shut down! ~*~*~*
Make sure to call shutdown()/shutdownNow()
java.lang.RuntimeException: ManagedChannel allocation site
at io.grpc.internal@1.63.0/io.grpc.internal.ManagedChannelOrphanWrapper$ManagedChannelReference.(ManagedChannelOrphanWrapper.java:102)
at io.grpc.internal@1.63.0/io.grpc.internal.ManagedChannelOrphanWrapper.(ManagedChannelOrphanWrapper.java:60)
at io.grpc.internal@1.63.0/io.grpc.internal.ManagedChannelOrphanWrapper.(ManagedChannelOrphanWrapper.java:51)
at io.grpc.internal@1.63.0/io.grpc.internal.ManagedChannelImplBuilder.build(ManagedChannelImplBuilder.java:672)
at io.grpc@1.63.0/io.grpc.ForwardingChannelBuilder2.build(ForwardingChannelBuilder2.java:260)
at org.apache.arrow.flight.core/org.apache.arrow.flight.TestServerOptions.addHealthCheckService(TestServerOptions.java:191)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:103)
at java.base/java.lang.reflect.Method.invoke(Method.java:580)
```

but those seems to only cause warnings, not errors

### Component(s)

FlightRPC, Java