Accessing file: protocol at chromium using XMLHttpRequest() or <link> element without --allow-file-access-from-files flag set at chromium instance launch is not enabled by default.
--allow-file-access-from-files
By default, file:// URIs cannot read other file:// URIs. This is an
  override for developers who need the old behavior for testing.
At the moment, due to the security policy Chromium can not read local
  files via ajax without --allow-file-access-from-files. But I
  currently need to create a web application where the database is a
  xml-file (in the extreme case, json), located in one dir with
  index.html. It is understood that the user can run this application
  locally. Are there workarounds for reading xml- (json-) file, without
  wrapping it in a function and change to js extension?
If user is aware that local files are to be used by the application you can utilize <input type="file"> element for user to upload file from user local filesystem, process file using FileReader, then proceed with application.
Else, advise user that use of application requires launching chromium with  --allow-file-access-from-files flag set, which can be done by creating a launcher for this purpose, specifying a different user data directory for the instance of chromium. The launcher could be, for example
/usr/bin/chromium-browser --user-data-dir="/home/user/.config/chromium-temp" --allow-file-access-from-files
See also How do I make the Google Chrome flag “--allow-file-access-from-files” permanent?
The above command could also be run at terminal 
$ /usr/bin/chromium-browser --user-data-dir="/home/user/.config/chromium-temp" --allow-file-access-from-files
without creating a desktop launcher; where when the instance of chromium is closed run
$ rm -rf /home/user/.config/chromium-temp
to remove the configuration folder for the instance of chromium.
Once the flag is set, user can include <link> element with rel="import" attribute and href pointing to local file and type set to "application/xml", for option other than XMLHttpRequest to get file. Access XML document using
const doc = document.querySelector("link[rel=import]").import;
See Is there a way to know if a link/script is still pending or has it failed.
Another alternative, though more involved, would be to use requestFileSystem to to store the file at LocalFileSystem.
See 
Or create or modify a chrome app and use 
chrome.fileSystem
See GoogleChrome/chrome-app-samples/filesystem-access.
The simplest approach would be to provide a means for file upload by affirmative user action; process the uploaded file, then proceed with the application.
const reader = new FileReader;
const parser = new DOMParser;
const startApp = function startApp(xml) {
  return Promise.resolve(xml || doc)
};
const fileUpload = document.getElementById("fileupload");
const label = document.querySelector("label[for=fileupload]");
const handleAppStart = function handleStartApp(xml) {
  console.log("xml document:", xml);
  label.innerHTML = currentFileName + " successfully uploaded";
  // do app stuff
}
const handleError = function handleError(err) {
  console.error(err)
}
let doc;
let currentFileName;
reader.addEventListener("loadend", handleFileRead);
reader.addEventListener("error", handleError);
function handleFileRead(event) {
  label.innerHTML = "";
  currentFileName = "";
  try {
    doc = parser.parseFromString(reader.result, "application/xml");
    fileUpload.value = "";
    startApp(doc)
    .then(function(data) {
        handleAppStart(data)
    })
    .catch(handleError);
  } catch (e) {
    handleError(e);
  }
}
function handleFileUpload(event) {
  let file = fileUpload.files[0];
  if (/xml/.test(file.type)) {
    reader.readAsText(file);
    currentFileName = file.name;
  }
}
fileUpload.addEventListener("change", handleFileUpload)
<input type="file" name="fileupload" id="fileupload" accept=".xml" />
<label for="fileupload"></label>