You can perform that by performing a loop through the Array if emails and perform a filter to like bellow

let emails = [
  'test@t-online.de',
  'kontakt@test.de',
  'info@test.de',
  'test@gmx.de',
  'kontakt@test.de',
];

let result = emails.reduce((accumulator, current) => {
  if(accumulator.indexOf(current) ===  -1){
    accumulator = accumulator.concat(current);
  }
  return accumulator;
}, []);

console.log(result);

Replace list with [...(new Set(list))].join('\n')

• new Set() ensures only duplicates are removed and only unique elements remain.
• join('\n') transforms the Array into a string separated by new-line (\n) character.

const list = [
  'test@t-online.de',
  'kontakt@test.de',
  'info@test.de',
  'test@gmx.de',
  'kontakt@test.de',
];
console.log([...(new Set(list))].join('\n'));

for removing duplicated emails:

arr = [...new Set(arr)];

for writing

var writeStream = fs.createWriteStream('./results/test.txt');
writeStream.on('error', function(e) { 
  /* handel error here */ 
});
arr.forEach(email => writeStream.write(email + '\n'));
writeStream.end();

To append data to an existed file Create write stream in append mode

var writeStream = fs.createWriteStream('./results/test.txt', { 'flags': 'a', 'encoding': null, 'mode': 0666});

refer here