[C++][Flight] Segmentation fault on arrow-flight-integration-test on nightly failure

arrow-flight-integration-test raised a segmentation fault failure on [verify-rc-source-python-linux-almalinux-8-amd64:](https://github.com/ursacomputing/crossbow/runs/7938987155?check_suite_focus=true)
```java

 54/90 Test #55: arrow-flight-integration-test .............***Failed    0.30 sec
Running arrow-flight-integration-test, redirecting output into /tmp/arrow-HEAD.cBR1G/cpp-build/build/test-logs/arrow-flight-integration-test.txt (attempt 1/1)
/arrow/cpp/build-support/run-test.sh: line 88: 25415 Segmentation fault      (core dumped) $TEST_EXECUTABLE "$@" > $LOGFILE.raw 2>&1
Running main() from /tmp/arrow-HEAD.cBR1G/cpp-build/googletest_ep-prefix/src/googletest_ep/googletest/src/gtest_main.cc
[==========] Running 3 tests from 1 test suite.
[----------] Global test environment set-up.
[----------] 3 tests from FlightIntegration
[ RUN      ] FlightIntegration.AuthBasicProto
[       OK ] FlightIntegration.AuthBasicProto (2 ms)
[ RUN      ] FlightIntegration.Middleware
Headers received successfully on failing call.
Headers received successfully on passing call.
[       OK ] FlightIntegration.Middleware (1 ms)
[ RUN      ] FlightIntegration.FlightSql
/tmp/arrow-HEAD.cBR1G/cpp-build/src/arrow/flight/integration_tests
```

**Reporter**: [Raúl Cumplido](https://issues.apache.org/jira/browse/ARROW-17493) / @raulcd

_{**Note**: *This issue was originally created as [ARROW-17493](https://issues.apache.org/jira/browse/ARROW-17493). Please see the [migration documentation](https://github.com/apache/arrow/issues/14542) for further details.*}

Start with the arrow-flight-integration-test failure log from the linked nightly run, focusing on FlightIntegration.FlightSql after the preceding tests pass. Trace the failing integration-test entry point and reproduce the crash; done means the test completes without a segmentation fault and the nightly test passes.

Written by the indexing model from the issue text.