extract.js

const {value, height} = this.state;

fullfile.js

export default class YourComponent extends Component {

  constructor (props) {
    super(props);
    this.state = {
      newValue: '',
      height: 40
    }
  }

  updateSize = (height) => {
    this.setState({
      height
    });
  }

  render () {
    const {newValue, height} = this.state;

    let newStyle = {
      height
    }

    return (
    <TextInput
      placeholder="Your Placeholder"
      onChangeText={(value) => this.setState({value})}
      style={[newStyle]}
      editable={true}
      multiline={true}
      value={value}
      onContentSizeChange={(e) => this.updateSize(e.nativeEvent.contentSize.height)}
    />
    )
  }

}

import.js

import {
  TextInput
} from 'react-native';

newStyle.js

const {value, height} = this.state;

let newStyle = {
  height
}

state.js

this.state = {
  value: '',
  height: 40
}

TextInput.jsx

<TextInput
  placeholder="Your Placeholder"
  onChangeText={(value) => this.setState({value})}
  style={[newStyle]}
  editable={true}
  multiline={true}
  value={value}
  onContentSizeChange={(e) => this.updateSize(e.nativeEvent.contentSize.height)}
/>

updateSize.js

updateSize = (height) => {
  this.setState({
    height
  });
}