Green’s Dictionary of Slang

(UK juv.) an insult aimed at one who wears a corrective brace on their teeth.

1998		Charlotte Obs. (NC) 10 Aug. 12: Share your happy or horrifying tinsel-tooth tales [...] ‘Yo! Metal Mouth,’ ‘ [...] ‘Hiya, Brace Face’.
2001		OnLine Dict. of Playground Sl. 🌐 brace-face n. rude name for someone wearing braces on their teeth.