Is there a Naruto manga that goes over kid Kakashi? I know some of kid Kakashi's story from Naruto: Ultimate Ninja Storm games but I would really like to read more about it.

Is there a Naruto manga that goes over kid Kakashi?
Let me help you.

You can read Kakashi Gaiden which covers his backstory when he was a kid. You can watch 119 to 120 of Naruto Shippuden also. I would suggest if you have and interest in Naruto the series and want to see where the characters started and orignated, watch Naruto and then Shippuden.