I wanted to answer this exact question so I made a very small demo of how to get the date of the latest commit.
Demo
Output:
ta-dachi
master
2019-03-21T14:50:22Z <----- What you want
b80126c3ea900cd7c92729e652b2e8214ff014d8
https://github.com/ta-dachi/eatsleepcode.tech/tree/master
Github repo
index.html
<head>
  <meta charset="UTF-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  <meta http-equiv="X-UA-Compatible" content="ie=edge" />
  <title>React Local</title>
  <script
    type="application/javascript"
    src="https://unpkg.com/react@16.0.0/umd/react.production.min.js"
  ></script>
  <script
    type="application/javascript"
    src="https://unpkg.com/react-dom@16.0.0/umd/react-dom.production.min.js"
  ></script>
  <script
    type="application/javascript"
    src="https://unpkg.com/@babel/standalone/babel.min.js"
  ></script>
  <script
    type="application/javascript"
    src="https://unpkg.com/whatwg-fetch@3.0.0/dist/fetch.umd.js"
  ></script>
</head>
<body>
  <div id="root"></div>
  <script type="text/jsx" src="index.jsx"></script>
</body>
index.jsx
/**
 * See https://developer.github.com/v3/repos/branches/#get-branch
 *
 * Example Github api request:
 * https://api.github.com/repos/ta-dachi/eatsleepcode.tech/branches/master
 */
class LatestCommitComponent extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      author: "",
      branch: "",
      date: "",
      sha: "",
      link: ""
    };
  }
  componentDidMount() {
    // Replace this with your own repo
    // https://api.github.com/repos/:owner/:repo/branches/master
    fetch(
      "https://api.github.com/repos/ta-dachi/eatsleepcode.tech/branches/master"
    )
      .then(response => {
        response.json().then(json => {
          console.log(json);
          this.setState({
            author: json.commit.author.login,
            branch: json.name,
            date: json.commit.commit.author.date,
            sha: json.commit.sha,
            link: json._links.html
          });
        });
      })
      .catch(error => {
        console.log(error);
      });
  }
  render() {
    return (
      <div>
        <div>{this.state.author}</div>
        <div>{this.state.branch}</div>
        <div>{this.state.date}</div>
        <div>{this.state.sha}</div>
        <div>{this.state.link}</div>
      </div>
    );
  }
}
ReactDOM.render(<LatestCommitComponent />, document.getElementById("root"));