mithril vest

[the phantom]

Thranduil wasn't the only one who made a statement about the mail being made for an elf-prince.

From The Hobbit-

"Mr. Baggins!" he (Thorin) cried. "Here is the first payment of your reward! Cast off your old coat and put on this!"
With that he put on Bilbo a small coat of mail, wrought for some young elf-prince long ago.

So Thranduil's statement does not stand alone. The narration backs him up.

But do we know for certain that Legolas had no brothers?