Make our own convenient OverlayContainer. The trick is to use absolute with 100% size (cf : https://github.com/onmyway133/blog/issues/254)

overlay_container.js

// @flow

import React from 'react'
import { View, StyleSheet } from 'react-native'

type Props = {
  behind: React.Component,
  front: React.Component,
  under: React.Component
}

// Show something on top of other
export default class OverlayContainer extends React.Component<Props> {
  render() {
    const { behind, front, under } = this.props

    return (
      <View style={styles.container}>
        <View style={styles.center}>
          <View style={styles.behind}>
            {behind}
          </View>
          {front}
        </View>
        {under}
      </View>
    )
  }
}

const styles = StyleSheet.create({
  container: {
    flex: 1,
    alignItems: 'center',
    height: 100,
    justifyContent: 'center',
  },
  center: {
    width: '100%',
    height: '100%',
    alignItems: 'center',
    justifyContent: 'center',
  },
  behind: {
    alignItems: 'center',
    justifyContent: 'center',
    position: 'absolute',
    left: 0,
    top: 0,
    width: '100%',
    height: '100%'
  }
})