The Linux kernel is a complex and constantly evolving system, where each code change can impact different components of the system. Regression testing ensures that new changes do not affect existing functionality or introduce new defects. However, due to the complexity of the Linux kernel, maintenance remains challenging. While practices like Continuous Integration (CI) facilitate rapid commits through automated regression testing, each CI process still incurs substantial costs due to the extensive number of test cases. Traditional software testing employs test case prioritization (TCP) techniques to prioritize test cases, thus enabling the early detection of defects. Due to the unique characteristics of the Linux kernel, it remains unclear whether the existing TCP techniques are suitable for its regression testing. In this paper, we present the first empirical study by comparing various TCP techniques in Linux kernel context. Specifically, we examined a total of 17 TCP techniques, including similarity-based, information-retrieval-based, and coverage-based techniques. The experimental results demonstrate that: (1) Similarity-based TCP techniques perform best on the Linux kernel, achieving a mean APFD (Average Percentage of Faults Detected) value of 0.7583 and requiring significantly less time; (2) The majority of TCP techniques show relatively stable performance across multiple commits, where similarity-based TCP techniques are more stable with a maximum decrease of 3.03% and 3.92% in terms of mean and median APFD values, respectively; (3) More than half of the studied techniques are significantly affected by flaky tests, with both mean and median APFD values ranging from -29.9% to -63.5%. This work takes the first look at the adoption of TCP techniques in the Linux kernel, confirming its potential for effective and efficient prioritization.