Forecasting time series with irregular temporal structures remains challenging for universal pre-trained models. Existing approaches often assume regular sampling or depend heavily on imputation, limiting their applicability in real-world scenarios where irregularities are prevalent due to diverse sensing devices and recording practices. We introduce FlexTSF, a flexible forecasting model specifically designed for time series data with variable temporal regularities. At its foundation lies the IVP Patcher, a continuous-time patching module leveraging Initial Value Problems (IVPs) to inherently support uneven time intervals, variable sequence lengths, and missing values. FlexTSF employs a decoder-only architecture that integrates normalized timestamp inputs and domain-specific statistics through a specialized causal self-attention mechanism, enabling adaptability across domains. Extensive experiments on 16 datasets demonstrate FlexTSF's effectiveness, significantly outperforming existing models in classic forecasting scenarios, zero-shot generalization, and low-resource fine-tuning conditions. Ablation studies confirm the contributions of each design component and the advantage of not relying on predefined fixed patch lengths.