I'm not sure if is this in an app. But this website is incredible with thousands of stories, classics.
The Baldwin Online Children's Literature Project. http://www.mainlesson.com
Another, Ambleside Online
They're amazing sites.
My Must Read App is a great app for short stories with attractive images. It offers a wide selection of short stories from around the world, with illustrations to match. The stories are categorized by age and difficulty, so you can find the ones that are perfect for your reading level. It also offers a selection of stories in different languages, so you can learn a new language while enjoying a good story.