We consider a communication system in which a given digital content has to be delivered sequentially at constant rate to a set of users who asynchronously request it according to a Poisson process. Users can retrieve data: i) from one or more sources that statically store the entire content; ii) from users who have previously requested the content, and contribute (for limited time) a random amount of upload bandwidth to the system. We propose a stochastic fluid framework that allows characterizing the aggregate streaming rate necessary at the sources to satisfy all active requests. In particular, we establish the conditions under which the system becomes asymptotically scalable as the number of users grows. Our theoretical results apply to increasingly popular Video-on-Demand systems exploiting users' cooperation.