The advent of 6G networks promises unprecedented advancements in mobile communication technology, offering ultra-low latency, enhanced reliability, and massive connectivity. Video streaming, a dominant use case, will significantly benefit from these advancements. However, managing buffer control to ensure seamless and high-quality video streaming in 6G remains a significant challenge. This paper explores buffer control mechanisms optimized for 6G environments, considering factors such as high data rates, network variability, and user mobility. We propose a dynamic buffer control algorithm that adapts to varying network conditions, ensuring minimal latency, high-resolution video quality, and uninterrupted playback. Our algorithm comprises key components including real-time network monitoring, predictive buffer management using machine learning models, mobility adaptation, and Quality of Experience (QoE) optimization. Through extensive simulations using a 6G network emulator, we demonstrate that our proposed algorithm significantly outperforms existing Adaptive Bitrate Streaming (ABR) algorithms in terms of reducing buffering events, enhancing video quality, and providing a smoother playback experience. The results underscore the potential of advanced buffer control mechanisms to fully exploit the capabilities of 6G technology, thereby enhancing the video streaming experience for end-users.