Kindness, Closeness
Noun and な adjective
こんい
その弁護士さんとはもう何十年も懇意にしていましてね。
I’ve been close to that lawyer for decades.
The idea of being courteous leads you to have more feelings of intimacy and kindness toward people. The more courteous someone is toward you (and vice versa), the more the closeness between the two of you grows.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.