Before Samuel anointed Saul, there were already quite a bit of interactions between the two.
1 Samuel 9:18 Saul approached Samuel in the gateway and asked, “Would you please tell me where the seer’s house is?” ...
19“I am the seer,” Samuel replied. “Go up before me to the high place, for you shall eat with me today. And when I send you off in the morning, I will tell you all that is in your heart. 20As for the donkeys you lost three days ago, do not worry about them, for they have been found. And upon whom is all the desire of Israel, if not upon you and all your father’s house?” ...
25And after they had come down from the high place into the city, Samuel spoke with Saul on the roof of his house.
26 They got up early in the morning, and just before dawn Samuel called to Saul on the roof, “Get ready, and I will send you on your way!” So Saul arose, and both he and Samuel went outside together.
They had known each other for a day. A friendship had started.
1 Samuel 10:1 Then Samuel took a flask of olive oil and poured it on Saul's head and kissed him, saying, "Has not the LORD anointed you ruler over his inheritance?
Samuel anointed Saul as a sign of respect and kissed him as a sign of friendship and affection.
When Samuel anointed David, they just met each other for the first time.
1 Samuel 16:11 So he asked Jesse, “Are these all the sons you have?”
“There is still the youngest,” Jesse answered. “He is tending the sheep.”
Samuel said, “Send for him; we will not sit down until he arrives.”
12So he sent for him and had him brought in. He was glowing with health and had a fine appearance and handsome features.
Then the Lord said, “Rise and anoint him; this is the one.”
13So Samuel took the horn of oil and anointed him in the presence of his brothers, and from that day on the Spirit of the Lord came powerfully upon David. Samuel then went to Ramah.
Samuel didn't kiss David here because they were not yet friends. They hadn't done things together before the anointing.
When Zadok anointed Solomon, he didn't kissed him either.
1 Kings 1:39 Zadok the priest took the horn of oil from the sacred tent and anointed Solomon. Then they sounded the trumpet and all the people shouted, "Long live King Solomon!"
The most famous friendship kiss in history is in Matthew 26:
49 Going at once to Jesus, Judas said, “Greetings, Rabbi!” and kissed him.
50 Jesus replied, “Do what you came for, friend.”