I use rn-fetch-blob, basically it provides lot of file system and network functions make transferring data pretty easy.

react-native-fetch-blob is deprecated

import RNFetchBlob from "rn-fetch-blob";

const fs = RNFetchBlob.fs;

let imagePath = null;

RNFetchBlob.config({

  fileCache: true

})

  .fetch("GET", "http://www.example.com/image.png")

  // the image is now dowloaded to device's storage

  .then(resp => {

    // the image path you can use it directly with Image component

    imagePath = resp.path();

    return resp.readFile("base64");

  })

  .then(base64Data => {

    // here's base64 encoded image

    console.log(base64Data);

    // remove the file from storage

    return fs.unlink(imagePath);

  });

source Project Wiki