Piece of clothing Kakashi wears under his grey Anbu flack jacket
It's categorized as a Jockey or Vest, according to their respective sales listing on Amazon. However, a Google search returns more relevant results when searching for '暗部ベスト'. Also, on Chiebukuro, Japan's Yahoo Answers, it is referred to as a 'vest'.

You can get it from Amazon Japan here. Use a shipping forwarding service like Tenso if you live outside Japan.