If photos aren't saving to your camera roll or gallery:
Make sure that you've turned on the Save Original Photos setting.
Filtered photos will only save to your camera roll after they've been uploaded to Instagram. Also, please be sure that you're using the latest version of the app, as we've fixed some bugs related to photo-saving in previous versions.
If your photos aren't saving after adjusting your Save Original Photos settings:
Check to make sure you have storage space on your phone. Open the Settings app, and on Android tap Storage. On iPhone, tap General > About. You'll see the amount of space you have left on your phone labeled as Available.
Restart your phone. This will help ensure there are no memory issues causing photo saving to fail.
You can also try these troubleshooting steps.
If the images still don't save to your phone, please file a bug report.