This study explores the synchronization of multimodal physiological data streams, in particular, the integration of electroencephalography (EEG) with a virtual reality (VR) headset featuring eye-tracking capabilities. A potential use case for the synchronized data streams is demonstrated by implementing a hybrid steady-state visually evoked potential (SSVEP) based brain-computer interface (BCI) speller within a fully immersive VR environment. The hardware latency analysis reveals an average offset of 36 ms between EEG and eye-tracking data streams and a mean jitter of 5.76 ms. The study further presents a proof of concept brain-computer interface (BCI) speller in VR, showcasing its potential for real-world applications. The findings highlight the feasibility of combining commercial EEG and VR technologies for neuroscientific research and open new avenues for studying brain activity in ecologically valid VR environments. Future research could focus on refining the synchronization methods and exploring applications in various contexts, such as learning and social interactions.