I'd recommend Pocket. It allows you to save short stories from the web. So, if you come across an interesting short story on a website, you can save it to Pocket and read it later at your convenience. It has a simple and clean interface.
Litrato is also a good app for short stories. It has a curated collection of short stories from both well - known and emerging authors. The app often features new and unique stories that you might not find elsewhere. Plus, it has a community where you can discuss the stories you've read with other users. This adds an extra layer of enjoyment to the reading experience.
Then there's Medium. While it's not solely dedicated to short stories, it has a plethora of short - form content, including many excellent short stories. Many professional and amateur writers publish their short works on Medium. You can follow different publications or writers to get a regular supply of interesting short stories. And the app is free to use, with an option to upgrade for additional features.