Is "Keeping to oneself" an American expression?
Also, is there a way to tell the difference between American Idioms and British ones?
"Keeping to oneself" is a formal way of describing this expression - most English speakers would rarely say "oneself". It is more commonly used something like this:
"I keep to myself"
"She keeps to herself"
"He kept to himself"
"They kept to themselves"
How can you tell the difference between American Idioms and British ones? Not easily just by reading them, although sometimes the choice of vocabulary gives something away. Perhaps try googling the phrase with the domain limited to US or UK websites. You might have to try variations on the phrase to get accurate results. Also, when you read any English text, keep in mind the nationality of the author - it can sometimes help you to learn which countries use which expressions.
Finally, I have no actual numbers, but I would guess that most idioms are used in both American and British English.