What did Uncle Jack learn from Scout and what does Atticus get them for Christmas?

Atticus buys his children air rifles.

As for the first part of your question, the following quote comes directly from the text.

“I know. Your daughter gave me my first lessons this afternoon. She said I didn’tunderstand children much and told me why. She was quite right. Atticus, she told me how I should have treated her—oh dear, I’m so sorry I romped on her.”