The actor for Kylo is in his early thirties, so I assumed his character is as well (which would also fit with the age of his parents), but I keep seeing people refer to him as a moody teenager (which may not be referring to age, but rather his manner). As for Rey, I assumed she was late teens/early twenties, but this is only backed up by how she behaves and her personality, not necessarily any facts.
Honestly I just want him to be old enough to support my theory that he
murdered younglings in front of a youngling Rey Skywalker!!!