個人比較傾向於利用螢幕寬度和高度以及relative相對距離來佈局。

/**
 * Sample React Native App
 * https://github.com/facebook/react-native
 * @flow
 */

import React, {Component} from 'react';
import {
    AppRegistry,
    StyleSheet,
    Text,
    View
} from 'react-native';

export default class Demo extends Component {
    render() {
        return
 
 (
            <View style={styles.container}>
                <View style={styles.navigationBar}>
                </View>
                {/*距離頂部40px,一個寬600px，高200px居中的View*/}
                <View style={[styles.sizeView,{position:'relative'}]}>
                </View>
                {/*距離左側20px,距離頂部80px,寬度400px,高度60px*/
 
}
                <View style={[styles.bottomLeftView,{position:'relative'}]}>
                </View>
                {/*距離bottomLeftView右側40px,距離頂部sizeView200px,寬度40px,高度200px*/}
                <View style={[styles.bottomRightView,{position:'relative'}]}>
                </View>
            </View>
        );
    }
}

let Dimensions = require('Dimensions'
 
);
let {width,height} = Dimensions.get('window');
let Platform = require('Platform');
let StatusBar = require('StatusBar');
{/*如果UI設計師的原型圖是以6S為基準，6S的螢幕寬度為1334畫素，那麼算出縮放比例*/}
let scale = width/1334;
let navHeight = Platform.OS === 'ios' ? 128*scale : StatusBar.currentHeight + 40*scale;


const styles = StyleSheet.create({
    container: {
        backgroundColor: 'yellow',
        width: width,
        height: height,
    },
    navigationBar: {
        backgroundColor: 'red',
        width:width,
        height:navHeight,
    },
    sizeView: {
        backgroundColor: 'green',
        marginTop: 40*scale,
        left: (width - 600*scale)/2,
        width: 600*scale,
        height: 200*scale,
    },
    bottomLeftView: {
        backgroundColor: 'blue',
        marginTop:80*scale,
        left: 20*scale,
        width: 400*scale,
        height: 60*scale,
    },
    bottomRightView: {
        backgroundColor: 'black',
        left: 20*scale + 400*scale + 40*scale,
        marginTop:200*scale,
        width: 40*scale,
        height: 200*scale,
    }
});

AppRegistry.registerComponent('Demo', () => Demo);

效果如圖：

相對距離根據需求可以換成螢幕寬高的百分比，這樣就可以適配各種解析度了。