Enable Flight / FlightSQL Integration Tests

**Is your feature request related to a problem or challenge? Please describe what you are trying to do.**

Archery provides Flight and FlightSQL Integration tests, we should enable these and fix any issues they turn up -
https://github.com/apache/arrow/blob/45b36976a31a4f363c0c471c2da1abd5bee97fd2/dev%2Farchery%2Farchery%2Fintegration%2Frunner.py#L689-L703

**Describe the solution you'd like**

**Describe alternatives you've considered**

**Additional context**

Start with dev/archery/archery/integration/runner.py at lines 689-703 and inspect how Flight and FlightSQL integration tests are currently handled. Enable those tests, run the integration suite, and use its failures to identify the issues that must be fixed before the tests pass.

Written by the indexing model from the issue text.