Yes, most of them are perfectly safe for machine washing and drying. However, we would advise you to look at the label before you do it, since the instructions may vary from one product to the other. You would usually wash it in a machine in warm water on a gentle cycle.
As for drying, it’s best to do it in a tumble dryer, on a low cycle. Hanging to dry is not recommended, because wet down tends to form into hard clusters. These clusters become too thick and difficult to break once the vest dries, which leads to cold spots because down isn’t equally spread. Tumble drying helps spread the down equally. If you want to learn more about how to maintain a down vest, be sure to read our article about washing a down jacket, because all the principles are basically the same.