I find myself using words like "kiddo", "bullshit" and "badass" in the more comedic side of dialogue/thoughts in my fantasy novel. At first it was simply me not paying attention, and not caring as I knew I'd edit it out in a later draft. But upon reading it, I found myself liking the contrast between modern speech and medieval-esque world. In an era of literary subversion, perhaps this is a welcoming addition? Or is this just stylistically untrue to the genre?
Quite a few narratives with a historic (or historic fantasy) setting employ modern references. An example is this intro to the movie A Knight's Tale, in which the spectators at a tournament clap their hands to Queen's "We will rock you".
What is the purpose of such a device?
Commonly writers aim to immerse their readers in their fictional world and make them forget that they are just reading a book, and – as @Amadeus has answered to a related question – the theory is that readers will find anachronisms jarring.
But that is not always true.
The common strategy of a writer is to provide the reader with the experience of being a person living in the time and setting of the narrative. That is, the reader is "immersed" in the narrative to feel what it might have been like to live in the middle ages.
But there is a different approach, and that is the approach taken by authors using anachronistic elements. These authors don't show their readers what it might have been like to live in the middle ages, but what it might be like if a person from our time were taken back to the middle ages – complete with their modern language and thinking and knowlege.
In some books (often called "portal fantasy") this is done explicitly: some person from today gets transported to the past or a parallel fantasy universe. But in some books this is done by using characters that live in the middle ages but act and speak as a we do.
Some readers find this jarring. Others enjoy the humorous effect.
In The Once and Future King, some knights drink port and consider sending some boys to Eton college. The narrator explains why he used these anachronisms:
It was not really Eton that he mentioned, for the College of Blessed Mary was not founded until 1440, but it was a place of the same sort. Also they were drinking Metheglyn, not Port, but by mentioning the modern wine it is easier to give you the feel.
More on anachronisms in art and literature: https://en.wikipedia.org/wiki/Anachronism#Art_and_literature
The language used in your story is supposed to communicate with your intended audience. As an example, in Fritz Lieber’s stories of the Fafhrd and the Grey Mouser, the author often used modern elements in his similes of action events — the severed head rolled down the street like a bowling bowl. It was never period descriptions, but given his audience in the pulp rag he published in, it was appropriate.
In your case, assuming your are not doing a portal story as has been described, you should use whatever vernacular you feel communicates the qualities and personalities of your characters to your intended audience.
It would be odd, and require explanation, if your POV characters were all kiddo and badass but the rest of the characters were speaking in Elizabethan prose or Shakespearian dialogue.
Not that all your characters have to speak the same way, we humies have always created and freely used language very liberally, often with short hand and vulgar terminology.
Its only important that the character’s dialogue seems appropriate for the scene they are in. If this kiddo slinger is talking informally and speaking in a vulgar and common manner, then there should be other characters speaking similarly at some time in the story. If your world has like formal speech — The King’s English or equivalent — and has a common tongue used by everyday people, then it would natural to expect that common tongue to be filled with slang, crudity, and pop-culture references to their times.