Not sure about Vitra production, but in the US the frames were/are polished aluminum with a clear coating that is often damaged especially at the arms. Looks like a vinyl sling on the chair in your link to me. Also, the tilt mechanism looks similar to the "Flo-Tilt" version from Herman Miller for which repair parts are long since unavailable.
Upholstery on Aluminum Group chairs is notorious for difficulty if not impossibility to effect satisfactory replacement without specialized skills and tools. I'd recommend seeking advice from Vitra regarding repairs or waiting for another chair in better condition to present itself.
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