It also took me a lot of time ... with better information it would be 5 minutes!
I use response-native-fs to get directories (which works for ios and android):
var RNFS = require('react-native-fs');
RNFS.DocumentDirectoryPath then returns something like '/var/mobile/Containers/Data/Application/15AC1CC6-8CFF-48F0-AFFD-949368383ACB/Documents'on iOS
Image :
<Image
style={{width:100, height:100}}
source={{uri: 'file://' + RNFS.DocumentDirectoryPath + '/myAwesomeSubDir/my.png', scale:1}}
/>
, , URL- . base64 uri ( !).