The Cooling-Storage-Ring External-target Experiment (CEE) at Heavy Ion Research Facility in Lanzhou (HIRFL) is designed to study the properties of nuclear matter created in heavy-ion collisions at a few hundred MeV/$u$ to 1 GeV/$u$ beam energies, facilitating the research of quantum chromodynamics phase structure in the high-baryon-density region. Collective flow is one of the most important observables in heavy-ion collision experiments to study the bulk behavior of the created matter. Even though the standard event plane method has been widely used for collective flow measurements, it remains crucial to validate and optimize this method for the CEE spectrometer. In this paper, we study the experimental procedures of measuring directed flow in $^{238}$U+$^{238}$U collisions at 500 MeV/$u$ using event planes reconstructed by Multi Wire Drift Chamber and Zero Degree Calorimeter, respectively. Jet AA Microscopic (JAM) transport generator is used to generate events, and the detector response is simulated by the CEE Fast Simulation (CFS) package. Finally, the optimal kinetic region for proton directed flow measurements is discussed for the future CEE experiment.