You can view your videos and images directly on your phone by going to My Content. All your videos and pictures are stored here, most recent at the top of the list. Just select the one you want to view.
You can now export ION360 photos and videos to your iPhone's Photos library. Select "Photo Library" from the sharing menu and a copy will be stored to Photos. iOS won't show the content in a 360 view, but some services that support 360 viewing will retain the 360 format if you share from Photos.