Actually, you can link text frames that have content in them. When you do, the content in the latter frames will move to the end of the frame.
To link two frames (with or without content), simply click with one of the selection tools on the outflow box (the little box near the lower right) of the 1st frame in your series, then click inside the next frame you want linked.
In your case, if you click and link frames with text in them, all of the story's text will be linked then you can delete the other text frames and just work with the first frame.
Hope that makes sense...