For many developing countries, COVID-19 vaccination roll-out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy-makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run smoothly and without delays. We propose a stochastic-dynamic facility location model that allows policy-makers to choose vaccination facilities while accounting for possible facility failure. The model is a multi-stage stochastic variant of the classic facility location problem where disruption risk is modelled as a binary multivariate random process - a problem class that has not yet been studied in the extant literature. To solve the problem, we propose a novel approximate dynamic programming algorithm which trains the shadow price of opening a flood-prone facility on historical data, thereby alleviating the need to fit a stochastic model. We trained the model using rainfall data provided by the local government of several major cities in the Philippines which are exposed to multiple flooding events per year. Numerical results demonstrate that the solution approach yields approximately 30-40% lower cost than a baseline approach that does not consider the risk of flooding. Recommendations based on this model were implemented following a collaboration with two large cities in the Philippines which are exposed to multiple flooding events per year.