Floods are increasingly frequent natural disasters causing extensive human and economic damage, highlighting the critical need for rapid and accurate flood inundation mapping. While remote sensing technologies have advanced flood monitoring capabilities, operational challenges persist: single-sensor approaches face weather-dependent data availability and limited revisit periods, while multi-sensor fusion methods require substantial computational resources and large-scale labeled datasets. To address these limitations, this study introduces a novel sensor-flexible flood detection methodology by fine-tuning Presto, a lightweight ($\sim$0.4M parameters) multi-modal pre-trained transformer that processes both Synthetic Aperture Radar (SAR) and multispectral (MS) data at the pixel level. Our approach uniquely enables flood mapping using SAR-only, MS-only, or combined SAR+MS inputs through a single model architecture, addressing the critical operational need for rapid response with whatever sensor data becomes available first during disasters. We evaluated our method on the Sen1Floods11 dataset against the large-scale Prithvi-100M baseline ($\sim$100M parameters) across three realistic data availability scenarios. The proposed model achieved superior performance with an F1 score of 0.896 and mIoU of 0.886 in the optimal sensor-fusion scenario, outperforming the established baseline. Crucially, the model demonstrated robustness by maintaining effective performance in MS-only scenarios (F1: 0.893) and functional capabilities in challenging SAR-only conditions (F1: 0.718), confirming the advantage of multi-modal pre-training for operational flood mapping. Our parameter-efficient, sensor-flexible approach offers an accessible and robust solution for real-world disaster scenarios requiring immediate flood extent assessment regardless of sensor availability constraints.