Yes! There are a few ways to do this...
If you're an on-the-go Sparkle subscriber, and you want to listen to stories offline, you can download stories to your Storybox in the iOS app. On the stories you choose, click the cloud icon to pull the stories onto your phone. Listen wherever, whenever, as long as you're a subscriber.
If you'd like to download and own the stories for good, you can do so by purchasing them through the Sparkle Shop. Once purchased, you can download them to a computer by clicking the download link in the receipt email you received. They're now yours! Keep them on your computer, download them to iTunes or another music player and listen on your phone, upload them to a CD or a flash drive for safekeeping — the Sparkle world is your oyster!