iPhone

You can manually add photos from any album available in your Photos app besides your regular Camera Roll. This would include iCloud or other any other app that creates an album in the Photos app (e.g. Instagram).

Android

You can import photos from anywhere on your device, including mostly cloud services such as Google Photos or Dropbox.

Website

You can only add photos directly from your computer files and cannot import them from other places, such as iCloud, Google Photos, Facebook, or anything of the kind (unless these are linked to your local files).