O que significa I want to flinch. (after saying sth kind of embarassing) ?

See a translation

flinching is more like a "shying away" kind of action rather than actually escaping, the action is the way you move when you feel like you're about to get hit, like you're hiding away. To be honest I've never seen "flinch" in context of the sentence used that way before. I don't know if it's because it's a translated sentence but usually after someone says something embarrassing, especially in my school, they'll say "I want to hide away" or just "I want to hide", either way you can think of it the same way a pet will hit its head against a window and hide its head under a blanket like you can't see them - not really gone or hidden, but they'll definitely wish you couldn't see them anymore