Unfortunately I can't get KeyboardAvoidingView working so I'm trying to handle the problem by myself. So I'm listening on keyboard events and update my component's state consequently! My problem is that the keyboard is closing when setState function trigger a re-render.

class MyComponent extends Component {
 state = {
    isKeyboardOpen: false
  };

 componentWillMount() {
    this.keyboardDidShowListener = Keyboard.addListener('keyboardDidShow', () =>
      this.setState({ isKeyboardOpen: true })
    );
    this.keyboardDidHideListener = Keyboard.addListener('keyboardDidHide', () =>
      this.setState({ isKeyboardOpen: false })
    );
  }

  componentWillUnmount () {
    this.keyboardDidShowListener.remove();
    this.keyboardDidHideListener.remove();
  }

render () {
  const {isKeyboardOpen } = this.state
  return (
    <TextInput style={{bottom: isKeyboardOpen: 150 : 0 }} />
 )
}

React Native version:

React Native Environment Info:
System:
OS: macOS 10.14.5
CPU: (4) x64 Intel(R) Core(TM) i7-7660U CPU @ 2.50GHz
Memory: 1.45 GB / 16.00 GB
Shell: 3.2.57 - /bin/bash
Binaries:
Node: 12.3.0 - /usr/local/bin/node
Yarn: 1.16.0 - /usr/local/bin/yarn
npm: 6.9.0 - /usr/local/bin/npm
Watchman: 4.9.0 - /usr/local/bin/watchman
SDKs:
iOS SDK:
Platforms: iOS 12.2, macOS 10.14, tvOS 12.2, watchOS 5.2
IDEs:
Android Studio: 3.4 AI-183.6156.11.34.5522156
Xcode: 10.2.1/10E1001 - /usr/bin/xcodebuild
npmPackages:
react: 16.8.3 => 16.8.3
react-native: 0.59.9 => 0.59.9

I didn't test on Android, thanks for your help!