Example react Native App that lets the user select an image from the image library and then syncs it to the icloud documents folder. The other device checks if the file is in the cloud and lets the user download it from the cloud to the device. It uses the icloud key/value store to store and sync the filename.
Follow installation instructions for React Native Image Picker: https://github.com/react-native-image-picker/react-native-image-picker
For ICloud Documents you need to add an iCloud Container here: https://developer.apple.com/account/resources/identifiers/list