Please use react-native-webview instead! While I haven't tested it myself yet, they have added Android file upload support as of v2.10.0 and are likely much better supported.
This is a demo project based off of the work of several others (such as this webview file upload sample code and this sample about overriding the built-in webview) to implement file upload in the React Native Android WebView.
Ideally all the changes to get it to work (from a basic RN project) should be in a single commit that you can put in your app.)
My particular use-case is focused on pictures, so I limited it to uploading from the camera and images already stored on the device. General file upload shouldn't be significantly different.
It only works with React Native 0.50+, and reverts to the built-in WebView on iOS.
I'm a newbie at Java, so I expect the code could use some improvement. :-D
NOTE: At least one version of the Android simulator doesn't seem to do the file upload correctly (it gives a checkered background with a red box instead of showing the file you uploaded), but it appears to work fine on the device. If you know what's going on there, I'd love to hear!