Your FlipaClip projects are saved locally on the device that you created the project on. They are not synced with any other devices that you may have FlipaClip installed on and they will not transfer if you upgrade or change devices. The best way to make sure that your projects stay safe is to share the project with a third party storage service such as Google Drive or iCloud Drive.
Signing into your account on the FlipaClip does not save your projects. Your FlipaClip account is specifically used for contest purposes.