A nice alternative to train or car when traveling to Traunkirchen is to take the ferry from any of the many stops along the Traunsee. The Ferry stops in places like Gmunden and Ebensee which should make getting to Traunkirchen a very relaxing and enjoyable trip along the Traunsee.
Fortunately for those backpacking across Europe or at the very least, without a car, you can take a train to Traunkirchen. Traunkirchen Ort (the name of the stop) is on the North-South line (which runs from Attnang-Puchheim to Stainach-Irdning) and is approximately 12 km from Gmunden. From this unstaffed train station, it's about a 5 minute walk down to the city center. There is another train stop (a main one) for the town a bit north of the town. This one is much better though because you're just minutes from the town center and the view from here is quite lovely.