isn't the literal translation "better not to say nothing"? (I know that's not what it means, I'm actually just curious why it sounds that way)
No. The word "כלום" means "something" or "anything". It's rarely used other than in the negative, but this is not a case of a double negative.
A similar word is "שום" as in "לא עשיתי שום דבר". The word means "any", but it's almost only used in the negative.