Multiple exposure speckle imaging has demonstrated its improved accuracy compared to single exposure speckle imaging for relative quantitation of blood flow in vivo. However, the calculation of blood flow maps relies on a pixelwise non-linear fit of a multi-parametric model to the speckle contrasts. This approach has two major drawbacks. First, it is computer-intensive and prevents real time imaging and, second, the mathematical model is not universal and should in principle be adapted to the type of blood vessels. We evaluated a model-free machine learning approach based on a convolutional neural network as an alternative to the non-linear fit approach. A network was designed and trained with annotated speckle contrast data from microfluidic experiments. The neural network performances are then compared to the non-linear fit approach applied to in vitro and in vivo data. The study demonstrates the potential of convolutional networks to provide relative blood flow maps from multiple exposure speckle data in real time.