The rapid advancement of large language models (LLMs) has exacerbated the memory bottleneck due to the widening gap between model parameter scaling and hardware capabilities. While post-training quantization techniques effectively reduce memory overhead, existing methods predominantly rely on static quantization strategies, which struggle to adapt to dynamic workloads. To address this, we propose FlexQuant, a dynamic precision-switching framework that optimizes the trade-off between inference speed and accuracy. Leveraging model perplexity entropy and Kullback-Leibler divergence, FlexQuant enables fine-grained, layer-wise mixed-precision quantization and dynamically adjusts bit-widths during each token generation. FlexQuant provides a comprehensive analysis of quantization strategies, introduces a precision requirement model for optimal switching, and implements efficient fine-grained precision management. Evaluations demonstrate that FlexQuant achieves a 1.3× end-to-end speedup across diverse language tasks with negligible accuracy loss introduced. This framework offers a flexible and adaptive solution for efficient LLM deployment.