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

We are seeing failures building Java within the archery integration test framework

https://github.com/apache/arrow-rs/actions/runs/4283526230/jobs/7459219738

Error:  /__w/arrow-rs/arrow-rs/java/flight/flight-core/src/test/java/org/apache/arrow/flight/client/CustomHeaderTest.java:[77,27] error: cannot find symbol
  symbol:   method getStartedServer((location)[...]ild())
  location: class FlightTestUtil

I've not dug deep into what is occurring here, but thought I would create a ticket in case this is a known issue / easy fix

Component(s)

Java