Yes, you can save your Swivl recorded videos on iOS device to your Camera roll IF it has not yet been uploaded to Reflectivity (Teams) web platform. Such a video is in Device Storage and has an orange icon on it.
If a Storage saver is enabled in the Settings of your Swivl Capture app, videos already uploaded to your Reflectivity (Teams) account cannot be saved to your Camera Roll. They are in Web Storage and have a blue cloud icon on it. To access them you need to log into your profile at cloud.swivl.com and look for them in Videos tab.
If you wish to keep the videos on your mobile device, see how to enable/disable the Auto upload feature in Navigating the Swivl Capture App: iOS
There is no option to save your video to the app gallery on Android devices. The video will still be accessible in file explorer.