React Native's Image component handles image caching like browsers for the most part. If the server is returning proper cache control headers for images you'll generally get the sort of built in caching behavior you'd have in a browser. Even so many people have noticed flickering, cache misses, low performance loading from cache and low performance in general.
FastImage is an Image replacement that solves these issues. FastImage is a wrapper around SDWebImage (iOS) and Glide (Android).