Recently, information-theoretic private information retrieval (PIR) from coded storage systems has gained a lot of attention, and a general star product PIR scheme was proposed. In this paper, the star product scheme is adopted, with appropriate modifications, to the case of private (e.g., video) streaming. It is assumed that the files to be streamed are stored on n servers in a coded form, and the streaming is carried out via a convolutional code. The star product is defined for this special case, and various properties are analyzed in the baseline case, with colluding servers, as well as with straggling and byzantine servers. The achievable PIR rates are derived for the given models.