This paper examines communities' accessibility to critical facilities such as hospitals, emergency medical services, and emergency shelters when facing flooding. We use travel speed reduction to account for flood-induced partial road failure. A modified betweenness centrality metric is also introduced to calculate the criticality of roads for connecting communities to critical facilities. The proposed model and metric are applied to the Delaware road network under 100-year floods. This model highlights the severe critical facility access loss risk due to flood isolation of facilities. The mapped post-flooding accessibility suggests a significant travel time increase to critical facilities and reveals disparities among communities, especially for vulnerable groups such as long-term care facility residents. We also identified critical roads that are vital for post-flooding access to critical facilities. The results of this research can help inform targeted infrastructure investment decisions and hazard mitigation strategies that contribute to equitable community resilience enhancement.