An example of using Dropbox API in Google Script

dropbox.gs

var token = '<PUT_YOUR_TOKEN_HERE>';

function dropboxAPI(path, data) {
 var response = UrlFetchApp.fetch('https://api.dropboxapi.com/2/' + path, {
    'method': 'POST',
    'payload': JSON.stringify(data),
    'headers': {
      'Authorization': 'Bearer ' + token,
      'Content-Type': 'application/json'
    },
    'muteHttpExceptions': true
  });

  if (parseInt(response.getResponseCode()) != 200) {
    return undefined;
  }

  return JSON.parse(response.getContentText());
}

function getFileByName(name) {
  var result = dropboxAPI('/files/search', {
    'path': '',
    'query': name,
    'start': 0,
    'max_results': 1,
    'mode': 'filename',
  });
  
  if (result) {
    return result.matches[0].metadata;
  }
  
  return undefined;
}

function getURLFromDropbox(name) {
  file = getFileByName(name);
  if (file === undefined) {
    return '';
  }
  
  var result = dropboxAPI('/files/get_temporary_link', {
    'path': file.path_lower,
  });

  if (result) {
    Logger.log('Successfully get a link:', result.link);
    return result.link;  
  }
  
  return '';
}

Using in Google SpreadSheet:

=IMAGE(getURLFromDropBox("part-of-image-filename"))

Screenshot: