If you are looking for something like:
imageSource.saveToGallery(name, extension);
I'm afraid there's nothing like that.
You will have to implement something custom for both Android and iOS to get the path to the gallery and save the image there.
Good news is there a plugin called nativescript-camera
that has an option to save the pictures you take to the gallery, so that should serve you as inspiration to implement what you need. Particularly, these two files:
You could actually create and publish your own nativescript-gallery
plugin to handle loading/saving images from/to the gallery!