Flaky tests are tests that can non-deterministically pass or fail, even in the absence of code changes. Despite being a source of false alarms, flaky tests often remain in test suites once they are detected, as they also may be relied upon to detect true failures. Hence, a key open problem in flaky test research is: How to quickly determine if a test failed due to flakiness, or if it detected a bug? The state-of-the-practice is for developers to re-run failing tests: if a test fails and then passes, it is flaky by definition; if the test persistently fails, it is likely a true failure. However, this approach can be both ineffective and inefficient. An alternate approach that developers may already use for triaging test failures is failure de-duplication, which matches newly discovered test failures to previously witnessed flaky and true failures. However, because flaky test failure symptoms might resemble those of true failures, there is a risk of missclassifying a true test failure as a flaky failure to be ignored. Using a dataset of 498 flaky tests from 22 open-source Java projects, we collect a large dataset of 230,439 failure messages (both flaky and not), allowing us to empirically investigate the efficacy of failure de-duplication. We find that for some projects, this approach is extremely effective (with 100\% specificity), while for other projects, the approach is entirely ineffective. By analyzing the characteristics of these flaky and non-flaky failures, we provide useful guidance on how developers should rely on this approach.