How is the timing chain involved with the workings of the transmission?

It is in no way involved with the trans. Complete opposite ends of the engine.


Why do you ask?

well i read that hard shifting can put strain on the timing chain and cause it to stretch.

hmm, I have never heard of that before.

He might mean the transmission drive chain? (link assembly drive?)

To an extent that can stress the timing chain but that is usually isolated to high mileage manual transmission cars, since the MT is a much more direct drive then the automatic is hard shifting can take a toll, however to date I only know of one person who has blown a timing chain due to hard shifting, and the car was around 200,000 as I recall.