The onset of plant flowering is one of many factors affected by climate change. This has important consequences for ecosystems, where plants and pollinators are at risk of a temporal mismatch. This also has implications for crops. The timing of their highest-sensitivity window is affected, despite some control exerted by agricultural management. Current efforts to monitor the onset of flowering rest on numerous but sparse ground observations, or on proxies like temperature models or vegetation indices. In crop studies, a time-invariant harvesting calendar is most widely used to infer the flowering period for crops. We use spectral data from satellite imagery, combined with convolutional neural networks, to create a large-scale, high-resolution proxy for the timing of flowering. We exploit a transfer learning method to overcome the sparsity of ground truth data on plant phenology. We first train a temporal convolutional neural network to predict a temperature-based proxy for flowering (the First Bloom Index from the National Phenology Network), using as input the 8-day composite from MODIS at a 500m resolution. This model learns relevant temporal patterns on both short and long time scales within a year, thanks to a dilated convolution structure. We then fine-tune the parameters from the last fully connected layer using ground observations from the National Phenology Network as training data. The root mean squared error of our model is about 8.6 days, though this average hides much spatial heterogeneity: in many places, the model performs well-enough to capture year-to-year variations, with a prediction within a couple days of the target, while it performs extremely poorly in a few places. Our model outperforms the temperature-based proxy since the latter has a root mean squared error of about 9.3 days on the same testing data. More importantly, our model extrapolates much better over space: it has a root mean squared error of about 12 days when predicting outside of our study region, compared to a 35-day error for the temperature-based model. This is a key feature, since our goal is to fill in the spatial gaps left by the sparse ground truth observations. These large-scale predictions of annual flowering times could offer insights into plant-pollinator desynchronization and crop calendar variation under climate change, and could be used for further applications like studying the health impacts of shifts in spring flowering times.