In modern English "I have one piece of advice to you" is strange. .. for you is normal. I have one piece of advice for you. I have one piece of advice to give you. .

Yup, it is for dramatic effect. Stone gives a piece of advice while making a bad sentence.

No worries, Michael. Now you don't think the little guy plays with words.

OK, now I've seen the clip, It's just a non-standard usage by the little guy. I misread your transcription: apologies :( He just makes a slip in the first instance, and corrects himself in the second. This is nothing to copy. (It is a comedy.)

You are right, it is definitely what is said. It looks like it is set in, maybe, the late 18th or early 19th century, so the language being used is quite formal and a little antiquated. It may have been a correct usage then (or maybe even now?), but it would sound very strange to a native speaker these days, I think. Either "I have a piece of advice to give you", or "I have a piece of advice; to you I say..." Would be correct (the later is quite pompous and may be what he is saying - but truncated). Personally I would say "for you", or "to give to you". Perhaps, though, someone else has a better understanding of using it in that way?