Blood flow monitoring is fundamental for assessing cardiovascular health and identifying vascular complications. Traditional Doppler ultrasound methods require bulky equipment and specialized expertise, while recent thermal sensing approaches face limitations due to blood vessel depth variability beneath the skin. We present a soft electronic platform that integrates multilayer thermal sensing with deep learning algorithms to simultaneously measure blood flow rate and vessel depth. The device uses a wireless system with thermal sensing modules, featuring strategically positioned thermistors in separate layers to capture thermal gradients at different heights from the skin surface. Deep learning processes multilayer thermal patterns to extract both parameters in real time. Validation through benchtop testing, finite element analysis, and on-body trials demonstrates accurate measurements across relevant flow rates and vessel depths. Integration with photoplethysmography enhances continuous blood pressure monitoring accuracy compared to conventional approaches, particularly during dynamic physiological changes. This technology offers potential for personalized cardiovascular monitoring, early detection of hemodynamic events, and skin graft surveillance.