Используйте для этого собственный компонент базовых карт.
import React, { Component } from 'react';
import { Image } from 'react-native';
import { Container, Header, Content, Card, CardItem, Thumbnail, Text, Button, Icon, Left, Body, Right } from 'native-base';
export default class CardImageExample extends Component {
render() {
return (
<Container>
<Header />
<Content>
<Card>
<CardItem>
<Left>
<Thumbnail source={{uri: 'Image URL'}} />
<Body>
<Text>NativeBase</Text>
<Text note>GeekyAnts</Text>
</Body>
</Left>
</CardItem>
<CardItem cardBody>
<Image source={{uri: 'Image URL'}} style={{height: 200, width: null, flex: 1}}/>
</CardItem>
<CardItem>
<Left>
<Button transparent>
<Icon active name="thumbs-up" />
<Text>12 Likes</Text>
</Button>
</Left>
<Body>
<Button transparent>
<Icon active name="chatbubbles" />
<Text>4 Comments</Text>
</Button>
</Body>
<Right>
<Text>11h ago</Text>
</Right>
</CardItem>
</Card>
</Content>
</Container>
);
}
}
Ссылка: - https://docs.nativebase.io/Components.html#card-image-headref