Jim is curious about a boxer and his father's conversation problem thinking it's easy as they have some family dispute and haven't talked to each other for a long time.
What is "talking part down pretty good"?
Jim- What is so hard about people just talking to each other?
Talk, listen, talk, listen.
Mel- Was it ever that simple for you and your parents?
Jim- Ok. We had the talking part down pretty good.
Pat | Define Pat at Dictionary.com
See the second sense of the word. It means "exactly to the point or purpose" or "learned, known, or mastered perfectly or exactly."
It's not really used in this way outside of phrases like "down pat" or "stand pat."