This paper presents a system for remote monitoring of respiration of individuals that can detect respiration rate, mode of breathing and identify coughing events. It comprises a series of polymer fabric-sensors incorporated into a sports vest, a wearable data acquisition platform and a novel rich internet application (RIA) which together enable remote real-time monitoring of untethered wearable systems for respiratory rehabilitation. This system will, for the first time, allow therapists to monitor and guide the respiratory efforts of patients in real-time through a web browser. Changes in abdomen expansion and contraction associated with respiration are detected by the fabric sensors and transmitted wirelessly via a Bluetooth-based solution to a standard computer. The respiratory signals are visualized locally through the RIA and subsequently published to a sensor streaming cloud-based server. A web-based signal streaming protocol makes the signals available as real-time streams to authorized subscribers over standard browsers. We demonstrate real-time streaming of a six-sensor shirt rendered remotely at 40 samples/s per sensor with perceptually acceptable latency (<0.5s) over realistic network conditions.