[Java] Handle exceptions when flight service processes put requests

The current way of processing is to swallow the exception silently and print a log. However, this way is not friendly to debugging and problem diagnosis. We need a way to process it explicitly. 

**Reporter**: [Liya Fan](https://issues.apache.org/jira/browse/ARROW-6056) / @liyafan82

_{**Note**: *This issue was originally created as [ARROW-6056](https://issues.apache.org/jira/browse/ARROW-6056). Please see the [migration documentation](https://github.com/apache/arrow/issues/14542) for further details.*}

Start by locating the Java Flight service entry point that processes put requests and the path that currently catches and logs exceptions. Determine the expected explicit handling from the surrounding service behavior; done means exceptions are no longer silently swallowed and the resulting behavior is covered by the project's existing checks.

Written by the indexing model from the issue text.