No way I know of in InDesign but what you could do is export all the content to an InCopy assignment. Open the assignment in InCopy and then check it out. That will give you all the stories to edit in Galley, Story or Layout view.
InCopy is a part of Creative Cloud. If you're on something earlier, there's little else I can offer unless you happen to be on CS6 since InCopy CS6 can still be purchased.
Another possibility might be to use the Text Stitch script from Rorohiko.com to thread the frames. You'd have to edit your paragraph styles so that the first paragraph in each frame has a keep option to start in next frame.
Thanks Bob Levine, I had not heard about InCopy. I will check it out.
Wondering what it would be. (just like I never understood the need for Fireworks! All I used it in earlier days was to create dropdown menus and slices).
Thanks Peter Spier, I will check this out too. I see that I will need such functionality more often. I will compare costing for this script vs InCopy.