Carly Kubacak from The BHW Group has written a comprehensive and well written guide to the React Native Camera Roll API.
Additionally she lists many Components and React Native APIs to cover this useful end to end scenario.

Accessing iPhone camera roll Images with React Native blog post

React Native is a framework for iPhone app development that uses native elements for the user interface and JavaScript to run and define the application logic. The framework exposes a subset of native iOS elements and also allows developers to create new, custom modules to perform actions that are not supported by the framework out of the box. The open source community has created a number of custom modules (icons, image picker, camera, etc.) that can be easily added to any React Native project.

There are multiple ways to access iPhone images using built-in React Native controls and custom modules. In this guide, I’ll cover how to use the React Native CameraRoll API to display a user's camera roll images and get the base64 encoded version of an image when it is selected. If you don’t have an existing React Native project, you can follow this guide to get started.