[Java][Flight] How can a FlightClient connect to multiple servers?

### Describe the usage question you have. Please include as many useful details as possible.

Our backend service is a cluster that allows clients to connect to any service. How does a FlightClient connect to multiple servers and maintain the authentication status. Our goal is load balancing. The server uses FlightService and grpc Server, but the authentication is in FlightService. I don't know how to maintain the authentication status of multiple servers in one FlightClient.

### Component(s)

Java

The issue names FlightClient, FlightService, and the gRPC Server; begin by tracing how the Java client handles connections and how authentication is established in FlightService. Determine whether multiple servers can be used while preserving authentication for load balancing; done means a documented, concrete answer or a clearly scoped follow-up.

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