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ARROW-15956: [Java] Consolidate Flight integration testing code

Also, report errors in integration tests to the client.
Hopefully, this will make debugging ARROW-15953 easier if we can
catch it happening again.

Closes #12650 from lidavidm/arrow-15956

Authored-by: David Li <li.davidm96@gmail.com>
Signed-off-by: David Li <li.davidm96@gmail.com>