Videos on Instagram stories are limited to 15 seconds but you can use an app to split a longer video into 15 second segments for your story and it then becomes the longer video.
Instead of recording 15 second videos for your story, simply record and edit a longer video (edit it using an app like Filmora Go). Then open your video in the Story cutter app (android) or the Storeo App (ios) and it will split it into 15 second videos which you can then easily share to your story. The result will be a longer than 15 second seamless looking video.
Storeo is currently only available for ios and Story cutter is available on Android.
Download the apps here