Non-deterministic test behavior, or flakiness, is common and dreaded among developers. Researchers have studied the issue and proposed approaches to mitigate it. However, the vast majority of previous work has only considered developer-written tests. The prevalence and nature of flaky tests produced by test generation tools remain largely unknown. We ask whether such tools also produce flaky tests and how these differ from developer-written ones. Furthermore, we evaluate mechanisms that suppress flaky test generation. We sample 6 356 projects written in Java or Python. For each project, we generate tests using EvoSuite (Java) and Pynguin (Python), and execute each test 200 times, looking for inconsistent outcomes. Our results show that flakiness is at least as common in generated tests as in developer-written tests. Nevertheless, existing flakiness suppression mechanisms implemented in EvoSuite are effective in alleviating this issue (71.7 % fewer flaky tests). Compared to developer-written flaky tests, the causes of generated flaky tests are distributed differently. Their non-deterministic behavior is more frequently caused by randomness, rather than by networking and concurrency. Using flakiness suppression, the remaining flaky tests differ significantly from any flakiness previously reported, where most are attributable to runtime optimizations and EvoSuite-internal resource thresholds. These insights, with the accompanying dataset, can help maintainers to improve test generation tools, give recommendations for developers using these tools, and serve as a foundation for future research in test flakiness or test generation.