Understanding gene perturbation effects across diverse cellular contexts is a central challenge in functional genomics, with important implications for therapeutic discovery and precision medicine. Single-cell technologies enable high-resolution measurement of transcriptional responses, but collecting such data is costly and time-consuming, especially when repeated for each cell type. Existing computational methods often require separate models per cell type, limiting scalability and generalization. We present CFM-GP, a method for cell type-agnostic gene perturbation prediction. CFM-GP learns a continuous, time-dependent transformation between unperturbed and perturbed gene expression distributions, conditioned on cell type, allowing a single model to predict across all cell types. Unlike prior approaches that use discrete modeling, CFM-GP employs a flow matching objective to capture perturbation dynamics in a scalable manner. We evaluate on five datasets: SARS-CoV-2 infection, IFN-beta stimulated PBMCs, glioblastoma treated with Panobinostat, lupus under IFN-beta stimulation, and Statefate progenitor fate mapping. CFM-GP consistently outperforms state-of-the-art baselines in R-squared and Spearman correlation, and pathway enrichment analysis confirms recovery of key biological pathways. These results demonstrate the robustness and biological fidelity of CFM-GP as a scalable solution for cross-cell type gene perturbation prediction.