Real-time LLM interactions demand streamed token generations, where text tokens are progressively generated and delivered to users while balancing two objectives: responsiveness (i.e., low time-to-first-token) and steady generation (i.e., required time-between-tokens). Standard LLM serving systems suffer from the inflexibility caused by non-preemptive request scheduling and reactive memory management, leading to poor resource utilization and low request processing parallelism under request bursts. Therefore, we present TokenFlow, a novel LLM serving system with enhanced text streaming performance via preemptive request scheduling and proactive key-value (KV) cache management. TokenFlow dynamically prioritizes requests based on real-time token buffer occupancy and token consumption rate, while actively transferring KV cache between GPU and CPU memory in the background and overlapping I/O with computation to minimize request preemption overhead. Extensive experiments on Llama3-8B and Qwen2.5-32B across multiple GPUs (RTX 4090, A6000, H200) demonstrate that TokenFlow achieves up to 82.5% higher effective throughput (accounting for actual user consumption) while reducing P99 TTFT by up to 80.2%, without degrading overall token throughput.