$\textbf{Objective:}$ Brain-predicted age difference (BrainAGE) is a neuroimaging biomarker reflecting brain health. However, training robust BrainAGE models requires large datasets, often restricted by privacy concerns. This study evaluates the performance of federated learning (FL) for BrainAGE estimation in ischemic stroke patients treated with mechanical thrombectomy, and investigates its association with clinical phenotypes and functional outcomes. $\textbf{Methods:}$ We used FLAIR brain images from 1674 stroke patients across 16 hospital centers. We implemented standard machine learning and deep learning models for BrainAGE estimates under three data management strategies: centralized learning (pooled data), FL (local training at each site), and single-site learning. We reported prediction errors and examined associations between BrainAGE and vascular risk factors (e.g., diabetes mellitus, hypertension, smoking), as well as functional outcomes at three months post-stroke. Logistic regression evaluated BrainAGE's predictive value for these outcomes, adjusting for age, sex, vascular risk factors, stroke severity, time between MRI and arterial puncture, prior intravenous thrombolysis, and recanalisation outcome. $\textbf{Results:}$ While centralized learning yielded the most accurate predictions, FL consistently outperformed single-site models. BrainAGE was significantly higher in patients with diabetes mellitus across all models. Comparisons between patients with good and poor functional outcomes, and multivariate predictions of these outcomes showed the significance of the association between BrainAGE and post-stroke recovery. $\textbf{Conclusion:}$ FL enables accurate age predictions without data centralization. The strong association between BrainAGE, vascular risk factors, and post-stroke recovery highlights its potential for prognostic modeling in stroke care.