It depends on context. If its very limited as you suggest simply logging some basic file transfer data processing the log once and throwing it away I would tend to be attracted to the flat file option as well. RDBMS would be a bit overkill however maybe forseeable future conciderations can add an overriding factor.
As a compromise you may want to think about an embedded solution like SQL Lite et al or using a database abstraction API (such as flat file ODBC driver) that operates on flat files and can later be easily changed to operate against an RDBMS without any or any siginficant code changes as conditions warrent.
You might also want to think in terms of log server such as using reliable syslog with database backed storage. With this method there is less complexity in the simple application and all systems can benefit from the arrangement.