data: [ {id: 0, key: 'Key1', checked: false }, ... }]

onCheckBoxChange(id) {
    let arr = Array.from(Object.create(this.state.data));
    arr[id].checked = !arr[id].checked;
    this.setState({
        data: arr
    })
 }

render() {
    return (
      <Container>
        <Content>
          <List dataArray={this.state.data}
            renderRow={(item) =>
                <View>
                    <ListItem>
                      <CheckBox checked={ this.state.data[item.id].checked }
                       onPress={()=> this.onCheckBoxChange(item.id)}/>
                <Text>{item.key}</Text>
              </ListItem>
            </View>
          }>
        </List>
      </Content>
    </Container>
    )
  }
}