Now that I have finished RTK1 (yay!) and have gotten my reps down to a manageable number, I am ready to start kanji chaining to learn the readings. However, I don't know where to find the readings. Does anyone have a list of the readings for RTK1 words that they could share with me?

There are lots of approaches to learning readings. I think some people would recommend the Core 2000 Anki deck. There's also Kanji in Context. Most people don't seem to use RTK2, although I did.